CUSAT CAT 2019 Question Paper M.Sc Statistics
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Page 1
CAT 2019 – STATISTICS
019
2
S T
E
1. T
If n is a positive integer, the number of terms in Binomial series
is N
O
SI
IS
(A n
)
M
(B) A
D
M
N
(C) O
M
SAT
M
(D Infinite
CO ) O
CU 2.
AT N
The coefficient of in the expansion of
19
is
S IO 0
(A 1
)
2
U S
(B) 0
(C)
ST
1 if n is even and 0 if n is odd
C IS E
(D 0 if n is even and 1 if n is odd
) T
N
O
S I
D
3. is valid if the value
of x is such that M
(A
) A−1 ≤ x ≤ 1
O
N
A
D
(B) −1< x <1
M
(C) −1< x ≤1 M
(D −1 ≤ x<1 C O
)
AT
S
CU
019
2
S T
E
1. T
If n is a positive integer, the number of terms in Binomial series
is N
O
SI
IS
(A n
)
M
(B) A
D
M
N
(C) O
M
SAT
M
(D Infinite
CO ) O
CU 2.
AT N
The coefficient of in the expansion of
19
is
S IO 0
(A 1
)
2
U S
(B) 0
(C)
ST
1 if n is even and 0 if n is odd
C IS E
(D 0 if n is even and 1 if n is odd
) T
N
O
S I
D
3. is valid if the value
of x is such that M
(A
) A−1 ≤ x ≤ 1
O
N
A
D
(B) −1< x <1
M
(C) −1< x ≤1 M
(D −1 ≤ x<1 C O
)
AT
S
CU
Page 2
0 19
4. Let Then the matrix2 A is
S T
TE
(A Singular
)
N
(B) Diagonal
O
SI
(C) Skew-symmetric
(D Symmetric IS
M
M
)
D
A
N
O
M
SA
T
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
4. Let Then the matrix2 A is
S T
TE
(A Singular
)
N
(B) Diagonal
O
SI
(C) Skew-symmetric
(D Symmetric IS
M
M
)
D
A
N
O
M
SA
T
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 3
5. Let A be a square matrix. If then the matrix A is
(A Symmetric 019
) 2
(B) Skew-symmetric S T
E
(C) Diagonal
(D Zero T
N
) O
SI
IS
M
A
D
M
N
6. Let O Then the matrix is a
M
M
O
(A Zero matrix
CO (B) Unit matrix
E
)
SAT
C T
(C) Symmetric matrix
T
(D Skew –symmetric matrix
CU
N
)
7. A
S IO
The rank of the matrix A= 0 1
[ 1 3 4 5 10|]
¿ 2
9
is
U S T
¿
S
C IS E
(A 2
)
T
(B) 5
N
(C) 1
O
(D
)
0
S I
D M
N
A
D
8. The Eigen values of a diagonal matrix
M are
(A M
)
C O
(B)
AT
S
CU
(A Symmetric 019
) 2
(B) Skew-symmetric S T
E
(C) Diagonal
(D Zero T
N
) O
SI
IS
M
A
D
M
N
6. Let O Then the matrix is a
M
M
O
(A Zero matrix
CO (B) Unit matrix
E
)
SAT
C T
(C) Symmetric matrix
T
(D Skew –symmetric matrix
CU
N
)
7. A
S IO
The rank of the matrix A= 0 1
[ 1 3 4 5 10|]
¿ 2
9
is
U S T
¿
S
C IS E
(A 2
)
T
(B) 5
N
(C) 1
O
(D
)
0
S I
D M
N
A
D
8. The Eigen values of a diagonal matrix
M are
(A M
)
C O
(B)
AT
S
CU
Page 4
(C)
019
(D
2
)
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
019
(D
2
)
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 5
( 1 2− 1|)( − 2 0 0|)
19
9. Product of the Eigen values of the matrix ¿ is
20 ¿
(A
)
1
S T
E
(B) 0 T
(C) 5 N
O
(D
)
10
SI
IS
M
Sum of the A
D
M
Eigen values of the matrix A=
( 11 1|) ( 12 2|)
10. is
N ¿
O ¿
M
O
(A 3
M
O
E
)
C (B) 6
SA T (C) 5
(D 4
C T
CU )
AT N 19
S IO 2 0
U
11. If then is equal to
(A
)
(B) rC IS
−r
S N
T E ST
O
M
(C) sin θ
IS
S I
(D
D
cos θ
M
A D
)
A
N
O
M
M
C O
AT
S
CU
19
9. Product of the Eigen values of the matrix ¿ is
20 ¿
(A
)
1
S T
E
(B) 0 T
(C) 5 N
O
(D
)
10
SI
IS
M
Sum of the A
D
M
Eigen values of the matrix A=
( 11 1|) ( 12 2|)
10. is
N ¿
O ¿
M
O
(A 3
M
O
E
)
C (B) 6
SA T (C) 5
(D 4
C T
CU )
AT N 19
S IO 2 0
U
11. If then is equal to
(A
)
(B) rC IS
−r
S N
T E ST
O
M
(C) sin θ
IS
S I
(D
D
cos θ
M
A D
)
A
N
O
M
M
C O
AT
S
CU
Page 6
19
f ( x)
12. If is even, then is equal to
20
(A
S T
E
)
T
N
O
(B) SI
IS
M
(C) A
D
M
N
O
(DM
A T
S 13.
CO
M
)
O
CU
T
The value of Γ (1)is
(A
A N 19
S IO 0
)
2
U S
(B) 0
(C) 1
ST
C IS E
(D 2
)
T
N
O
14.
S I
If Γ ( n+1)=90 Γn− 1, the value of n is
D
(A 9
)
M
A D
(B) 10
(C) 90 A
(D 19
N
)
O
M
15. The value of β (4,2) is M
C O
(A
)
1
10 AT
S
CU
f ( x)
12. If is even, then is equal to
20
(A
S T
E
)
T
N
O
(B) SI
IS
M
(C) A
D
M
N
O
(DM
A T
S 13.
CO
M
)
O
CU
T
The value of Γ (1)is
(A
A N 19
S IO 0
)
2
U S
(B) 0
(C) 1
ST
C IS E
(D 2
)
T
N
O
14.
S I
If Γ ( n+1)=90 Γn− 1, the value of n is
D
(A 9
)
M
A D
(B) 10
(C) 90 A
(D 19
N
)
O
M
15. The value of β (4,2) is M
C O
(A
)
1
10 AT
S
CU
Page 7
1
(B)
20
019
1 2
(C)
8
S T
E
(D 1 T
) 6 N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
(B)
20
019
1 2
(C)
8
S T
E
(D 1 T
) 6 N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 8
16. Which one of the following is not correct?
(A 1 019
)
Γ ()
2
=√ π 2
S T
E
(B) β (m , n)=β(n , m)
T
(C) Γn+1=(n −1)Γn N
O
SI
β (m , n)= IS
(D ΓmΓn
MΓm +n
M
)
D
A
N
17. O
Which one of the following is not a two dimensional diagram?
M
SA T
O
M
O
(A Square diagram
E
C )(B) Multiple bar diagram
C T
(C) Rectangular diagram
CU
T
(D Pie-chart
A N
)
19
18.
S IO 2 0
The A.M of two numbers is 6.5 and their G.M is 6. The two
U S
numbers are
ST
C IS E
(A 9, 6
) T
(B) 9, 5
N
O
M
(C) 7, 6
(D 4, 9
S I
IS
)
D M
A D
19. Mean deviation is minimum when deviations are taken from
A
(A Mean
N
)
O
(B) Median
M
(C) Mode
M
(D
)
Zero
C O
AT
20.
S
If each value of a series is multiplied by a constant C, the
U
coefficient of variation as compared to original value is
C
(A 1 019
)
Γ ()
2
=√ π 2
S T
E
(B) β (m , n)=β(n , m)
T
(C) Γn+1=(n −1)Γn N
O
SI
β (m , n)= IS
(D ΓmΓn
MΓm +n
M
)
D
A
N
17. O
Which one of the following is not a two dimensional diagram?
M
SA T
O
M
O
(A Square diagram
E
C )(B) Multiple bar diagram
C T
(C) Rectangular diagram
CU
T
(D Pie-chart
A N
)
19
18.
S IO 2 0
The A.M of two numbers is 6.5 and their G.M is 6. The two
U S
numbers are
ST
C IS E
(A 9, 6
) T
(B) 9, 5
N
O
M
(C) 7, 6
(D 4, 9
S I
IS
)
D M
A D
19. Mean deviation is minimum when deviations are taken from
A
(A Mean
N
)
O
(B) Median
M
(C) Mode
M
(D
)
Zero
C O
AT
20.
S
If each value of a series is multiplied by a constant C, the
U
coefficient of variation as compared to original value is
C
Page 9
(A Increased
19
)
(B)
(C)
Decreased
Unaltered 20
(D Zero
S T
E
)
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
19
)
(B)
(C)
Decreased
Unaltered 20
(D Zero
S T
E
)
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 10
21. If A ⊂ B , the probability, P( A /B) is equal to
(A Zero 019
) 2
S T
E
(B) One
T
(C) N
O
SI
(D
IS
M
M
)
D
A
N
22. O
If a number is selected randomly from each of the two sets
M
T
O
M
O
1, 2, 3, 4, 5, 6, 7, 8
C 2, 3, 4, 5, 6, 7, 8, 9
SA then the probability that the sum of the numbers is equal to 9 is
CU (A
AT N 19
S IO
)
(B) 2 0
(C)
(D
U
C IS S T E ST
N
)
O
S I
23. If
D andM , then is equal
to
(A
)
N
A
D
M
(B)
M
(C) C O
(D AT
S
)
CU
(A Zero 019
) 2
S T
E
(B) One
T
(C) N
O
SI
(D
IS
M
M
)
D
A
N
22. O
If a number is selected randomly from each of the two sets
M
T
O
M
O
1, 2, 3, 4, 5, 6, 7, 8
C 2, 3, 4, 5, 6, 7, 8, 9
SA then the probability that the sum of the numbers is equal to 9 is
CU (A
AT N 19
S IO
)
(B) 2 0
(C)
(D
U
C IS S T E ST
N
)
O
S I
23. If
D andM , then is equal
to
(A
)
N
A
D
M
(B)
M
(C) C O
(D AT
S
)
CU
Page 11
24. 019
If X is a random variable which can take only non-negative
values, then 2
S T
E
(A
) T
N
O
(B) SI
IS
M
M
(C)
D
(D NoneAof the above
N
)
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
If X is a random variable which can take only non-negative
values, then 2
S T
E
(A
) T
N
O
(B) SI
IS
M
M
(C)
D
(D NoneAof the above
N
)
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 12
25. Negative binomial distribution, NB(x ; r , p) for r =1 reduces to
(A Binomial distribution 019
) 2
(B) Poisson distribution
S T
E
(C) Hypergeometric distribution
(D Geometric distribution T
) N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
(A Binomial distribution 019
) 2
(B) Poisson distribution
S T
E
(C) Hypergeometric distribution
(D Geometric distribution T
) N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 13
26. An approximate relation between Q.D and S.D of a normal
distribution is
019
(A 5Q.D = 4 S.D 2
) S T
E
(B) 4 Q.D = 5 S.D
T
(C) 2 Q.D = 3 S.D N
O
(D 3 Q.D= 2 S.D
SI
)
IS
M
27.
D
M
Mode of theAchi-square distribution with n.d.f lies at the point
N
(A O
) M
SA T
M
CO (B) O
T
(C)
CU (D
A N 19
S IO
)
2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
distribution is
019
(A 5Q.D = 4 S.D 2
) S T
E
(B) 4 Q.D = 5 S.D
T
(C) 2 Q.D = 3 S.D N
O
(D 3 Q.D= 2 S.D
SI
)
IS
M
27.
D
M
Mode of theAchi-square distribution with n.d.f lies at the point
N
(A O
) M
SA T
M
CO (B) O
T
(C)
CU (D
A N 19
S IO
)
2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 14
28. Stratified sampling belongs to the category of
(A Judgement sampling 019
) 2
(B) Subjective sampling S T
E
(C) Controlled sampling
T
(D Non-random sampling N
O
)
SI
IS
M
D
M
29. Systematic sampling means
A of n contiguous units
N
(A Selection
) O
(B)M Selection of n units situated at equal distances
SAT
M
) O
(C) Selection of n largest units
CO (D Selection of n middle units in a sequence
CU 30.
AT
If an estimator
N of population parameter θ converges in
19
S IO
probability to θ as n tends to infinity then
2 0 is said to be
U S T
(A Sufficient
)
S
C IS E
(B) Efficient
(C) Consistent T
(D Unbiased
N
O
M I
)
S
IS
31.
D
Sample median as an estimator of population mean is always
M
(A
)
(B)
(C)
AUnbiased
Efficient
O
Sufficient
N
A
D
(D None of the above
M
)
M
C O
32.
T
The maximum likelihood estimators are necessarily
A
(A Unbiased
S
)
CU
(A Judgement sampling 019
) 2
(B) Subjective sampling S T
E
(C) Controlled sampling
T
(D Non-random sampling N
O
)
SI
IS
M
D
M
29. Systematic sampling means
A of n contiguous units
N
(A Selection
) O
(B)M Selection of n units situated at equal distances
SAT
M
) O
(C) Selection of n largest units
CO (D Selection of n middle units in a sequence
CU 30.
AT
If an estimator
N of population parameter θ converges in
19
S IO
probability to θ as n tends to infinity then
2 0 is said to be
U S T
(A Sufficient
)
S
C IS E
(B) Efficient
(C) Consistent T
(D Unbiased
N
O
M I
)
S
IS
31.
D
Sample median as an estimator of population mean is always
M
(A
)
(B)
(C)
AUnbiased
Efficient
O
Sufficient
N
A
D
(D None of the above
M
)
M
C O
32.
T
The maximum likelihood estimators are necessarily
A
(A Unbiased
S
)
CU
Page 15
(B) Sufficient
19
(C) Most efficient
(D Unique
) 20
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
19
(C) Most efficient
(D Unique
) 20
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 16
33. Degree of freedom is related to
(A Number of observations in a set 019
) 2
(B) Hypothesis under test
S T
E
(C) Number of independent observations in a set
(D None of the above T
) N
O
SI
34. ISin SPRT depends on the functions of
The decision criteria
M
D
(A TypeAI error
M
) N
(B) OType II error
(C)M Type I and II errors
SA
T
O
C )
M
O E
(D None of the two types of errors
C T
CU
T
35. Kolmogorov-Smirnov test is a
(A
A N
One left-sided test
19
S IO
)
(B) One right-sided test
2 0
U S
(C) Two-sided test
(D All of the above
ST
C IS E
)
T
N
36.
O
If the two lines of regression are coincident the relation between
M S I
the two regression coefficients is
IS
D
(A
) M
(B)
(C)
N
β YX ≤ β XY
A
β YX . β XY=1
D
β YX =− β XY M
(D
M
)
C O
A T
37.
S
If ρ=1, the relation between the two variables X and Y is
C U
(A Y is proportional of X
(A Number of observations in a set 019
) 2
(B) Hypothesis under test
S T
E
(C) Number of independent observations in a set
(D None of the above T
) N
O
SI
34. ISin SPRT depends on the functions of
The decision criteria
M
D
(A TypeAI error
M
) N
(B) OType II error
(C)M Type I and II errors
SA
T
O
C )
M
O E
(D None of the two types of errors
C T
CU
T
35. Kolmogorov-Smirnov test is a
(A
A N
One left-sided test
19
S IO
)
(B) One right-sided test
2 0
U S
(C) Two-sided test
(D All of the above
ST
C IS E
)
T
N
36.
O
If the two lines of regression are coincident the relation between
M S I
the two regression coefficients is
IS
D
(A
) M
(B)
(C)
N
β YX ≤ β XY
A
β YX . β XY=1
D
β YX =− β XY M
(D
M
)
C O
A T
37.
S
If ρ=1, the relation between the two variables X and Y is
C U
(A Y is proportional of X
Page 17
)
19
(B) Y is inversely proportional to X
(C) Y is equal to X
(D None of the above 20
)
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
19
(B) Y is inversely proportional to X
(C) Y is equal to X
(D None of the above 20
)
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 18
38. The consistent increase in production of cereals constitutes the
component of the time series
019
(A Secular trend 2
)
S T
E
(B) Seasonal variation
(C) Irregular variation T
N
(D All of the above
O
)
SI
IS
M
39. D
M
Combining of two index numbers series having different base
A
periods into one series with common base period is known as
N
O
(A Splicing
M
M
O
)
CO (C) Both (A) and (B)
E
(B) Base shifing
SAT (D
C T
Neither (A) nor (B)
T
)
CU
40.
A N 9
The graph of the proportion of defectives in the lot against
1
S IO
average sample number is
2 0
U S T
(A OC curve
) S
C IS E
(B) A.S.N curve
(C) Power curve T
(D All of the above N
O
M I
)
S
IS
41.
D
In the analysis of data of RBD with b block and v treatments,
M
A D
the error degrees of freedom are
(A b (v −1) A
N
)
O
(B) v (b −1) M
M
(C) (b − 1)( v − 1)
C O
(D
)
T
None of the above
A
S
CU
component of the time series
019
(A Secular trend 2
)
S T
E
(B) Seasonal variation
(C) Irregular variation T
N
(D All of the above
O
)
SI
IS
M
39. D
M
Combining of two index numbers series having different base
A
periods into one series with common base period is known as
N
O
(A Splicing
M
M
O
)
CO (C) Both (A) and (B)
E
(B) Base shifing
SAT (D
C T
Neither (A) nor (B)
T
)
CU
40.
A N 9
The graph of the proportion of defectives in the lot against
1
S IO
average sample number is
2 0
U S T
(A OC curve
) S
C IS E
(B) A.S.N curve
(C) Power curve T
(D All of the above N
O
M I
)
S
IS
41.
D
In the analysis of data of RBD with b block and v treatments,
M
A D
the error degrees of freedom are
(A b (v −1) A
N
)
O
(B) v (b −1) M
M
(C) (b − 1)( v − 1)
C O
(D
)
T
None of the above
A
S
CU
Page 19
42. If two Latin Square are such that one can be obtained by
19
interchanging the rows of one with columns of the other, then
0
the Latin squares are said to be
2
(A Conjugate S T
E
)
(B) Self conjugate T
N
(C) Orthogonal O
(D Asymmetric SI
) IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
19
interchanging the rows of one with columns of the other, then
0
the Latin squares are said to be
2
(A Conjugate S T
E
)
(B) Self conjugate T
N
(C) Orthogonal O
(D Asymmetric SI
) IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 20
43. The method of confounding is a device to reduce the size of
(A Experiments 019
) 2
(B) Replications
S T
E
(C) Blocks
(D All of the above T
) N
O
S I
44.
S
If X ~ b (n , p), the Idistribution of Y =(n − X) is
M
A
D
M
(A b (n ,1)
N
) O
M
M
O
(B) b (n , x )
SA T
CO (C) b (n , p)
T
(D
CU
N
)
45.
A
S IO 2
If X is Poisson variate with parameter
0 19
the moment
(A
)
U
C IS S T E
T
generating function of Poisson variate is
S
N
O
M I
(B)
S
IS
(C)
D M
(D
)
N
A
D
M
46. M of
The relation between the mean and variance with n.d.f is
(A Mean = 2 variance C O
)
(B) 2 mean = variance A
T
(C) Mean = varianceS
CU
(D None of the above
(A Experiments 019
) 2
(B) Replications
S T
E
(C) Blocks
(D All of the above T
) N
O
S I
44.
S
If X ~ b (n , p), the Idistribution of Y =(n − X) is
M
A
D
M
(A b (n ,1)
N
) O
M
M
O
(B) b (n , x )
SA T
CO (C) b (n , p)
T
(D
CU
N
)
45.
A
S IO 2
If X is Poisson variate with parameter
0 19
the moment
(A
)
U
C IS S T E
T
generating function of Poisson variate is
S
N
O
M I
(B)
S
IS
(C)
D M
(D
)
N
A
D
M
46. M of
The relation between the mean and variance with n.d.f is
(A Mean = 2 variance C O
)
(B) 2 mean = variance A
T
(C) Mean = varianceS
CU
(D None of the above
Page 21
)
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 22
47. If X and Y are distribution as with d.f and
9
1 is
0
respectively, the distribution of the variate
2
(A S T
TE
)
N
O
(B) S I
IS
M
(C) D
Awith df (
M )
(D All N of the above
) O
M
SA
M
T (A Negative skewed O
48. COF-distribution curve in respect of tails is
CU
T
)
N
(B) Positive skewed
) A
(C) Symmetrical
S IO
(D None of the above
2 0 19
49. U
C IS
The variable
follows
S T E ST
where x is distributed as U ( 0,1)
N
O
M I
(A F-distribution
) S
IS
D
(B) t-distribution
M
(C)
(D
)
A N
A
D
-distribution
Exponential distribution
O
M
Mnout of N population
50.
O
The number of possible samples of size
units without replacement is
C
(A ( N|) A T
¿ S
) ¿
C U
9
1 is
0
respectively, the distribution of the variate
2
(A S T
TE
)
N
O
(B) S I
IS
M
(C) D
Awith df (
M )
(D All N of the above
) O
M
SA
M
T (A Negative skewed O
48. COF-distribution curve in respect of tails is
CU
T
)
N
(B) Positive skewed
) A
(C) Symmetrical
S IO
(D None of the above
2 0 19
49. U
C IS
The variable
follows
S T E ST
where x is distributed as U ( 0,1)
N
O
M I
(A F-distribution
) S
IS
D
(B) t-distribution
M
(C)
(D
)
A N
A
D
-distribution
Exponential distribution
O
M
Mnout of N population
50.
O
The number of possible samples of size
units without replacement is
C
(A ( N|) A T
¿ S
) ¿
C U
Page 23
(B)
019
(C) 2
(D n! S T
E
) T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
019
(C) 2
(D n! S T
E
) T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 24
51. Probability of drawing a unit at each selection remains same in
(A srswor 019
) 2
(B) srswr
S T
E
(C) both (A) and (B)
(D None of (A) and (B) T
) N
O
SI
IS
M
M
52. If
D is a random sample from a population
A
N a sufficient statistic for is
(AM
O
SAT
M
)
CO (B) O
CU (C)
(D
AT N
None of the above
19
S IO 0
)
2
53.
(A
U
C IS S
Mean squared error of an estimator
T E ST of τ (θ)is expressed as
) N
O
(B)
S I
D M
A
(C)
D
(D A
N
)
O
M
M
54.
unbiased estimator through C O
Rao- Blackwell theorem enables us to obtain minimum variance
(A Unbiased estimators A T
S
)
C U
(B) Complete statistics
(A srswor 019
) 2
(B) srswr
S T
E
(C) both (A) and (B)
(D None of (A) and (B) T
) N
O
SI
IS
M
M
52. If
D is a random sample from a population
A
N a sufficient statistic for is
(AM
O
SAT
M
)
CO (B) O
CU (C)
(D
AT N
None of the above
19
S IO 0
)
2
53.
(A
U
C IS S
Mean squared error of an estimator
T E ST of τ (θ)is expressed as
) N
O
(B)
S I
D M
A
(C)
D
(D A
N
)
O
M
M
54.
unbiased estimator through C O
Rao- Blackwell theorem enables us to obtain minimum variance
(A Unbiased estimators A T
S
)
C U
(B) Complete statistics
Page 25
(C) Efficient statistics
19
(D Sufficient statistics
)
20
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
19
(D Sufficient statistics
)
20
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 26
55. If t is a consistent estimator of then
19
(A t is also a consistent estimator of20
)
S T
TE of θ
(B) is also a consistent estimator
N
O
(C)
SI estimator of
is also a consistent
(D None of theIabove S
M
M
)
D
A
N
56. O for the confidence interval for the ratio of variances of
Formula
twoMnormal population involves
SA
T
M
CO (A
) O
- distribution
CU
T
(B) F distribution
A N
(C) t -distribution
19
(D
)
S IO
None of the above
2 0
57.
U
C IS S T E
1
ST
For the distribution f ( x ; θ)= ; 0 ≤ x ≤θ a sufficient estimator
θ
N
O
M
for θ based on a sample
S I is
IS
D
(A
)
M
(B)
A
(C) max( O
N
A
D
M
)
M
(D
) min( )
C O
AT
S
CU
19
(A t is also a consistent estimator of20
)
S T
TE of θ
(B) is also a consistent estimator
N
O
(C)
SI estimator of
is also a consistent
(D None of theIabove S
M
M
)
D
A
N
56. O for the confidence interval for the ratio of variances of
Formula
twoMnormal population involves
SA
T
M
CO (A
) O
- distribution
CU
T
(B) F distribution
A N
(C) t -distribution
19
(D
)
S IO
None of the above
2 0
57.
U
C IS S T E
1
ST
For the distribution f ( x ; θ)= ; 0 ≤ x ≤θ a sufficient estimator
θ
N
O
M
for θ based on a sample
S I is
IS
D
(A
)
M
(B)
A
(C) max( O
N
A
D
M
)
M
(D
) min( )
C O
AT
S
CU
Page 27
58. A confidence interval of confidence coefficient (1 −α ) is best
which has
019
(A Smallest width 2
)
S T
E
(B) Vastest width
(C) T
Upper and lower limits equidistant from the parameter
N
(D
O
One-sided confidence interval
) SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
which has
019
(A Smallest width 2
)
S T
E
(B) Vastest width
(C) T
Upper and lower limits equidistant from the parameter
N
(D
O
One-sided confidence interval
) SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 28
59. If the variance of an estimator attains the Crammer-Rao lower
bound, the estimator is
019
(A Most efficient 2
)
S T
E
(B) Sufficient
(C) Consistent T
N
(D Admissible
O
)
SI
IS
M
60. D
M
Power of a test is related to
A
(A N I error
type
) O
M II error
M type
O
(B)
CO
E
(C)
type I and II errors both
C T
(D None of the above
AT )
S
CU 61.
AT N
A test based on a test statistic is classified as
19
S IO 0
(A Randomised test
)
2
U S
(B) Non-randomised test
(C) Sequential test
ST
C IS E
(D Bayes test
) T
N
O
62.
M S I
Neyman-Pearson lemma provides
IS
D
(A An unbiased test
) M
A D
(B) A most powerful test
(C) A
An admissible test
(D
N
Minimax test
)
O
M
Equality of several normal populationM
63.
C O means can be tested by
(A Bartlett’s test
)
A T
S
(B) F-test
C U
bound, the estimator is
019
(A Most efficient 2
)
S T
E
(B) Sufficient
(C) Consistent T
N
(D Admissible
O
)
SI
IS
M
60. D
M
Power of a test is related to
A
(A N I error
type
) O
M II error
M type
O
(B)
CO
E
(C)
type I and II errors both
C T
(D None of the above
AT )
S
CU 61.
AT N
A test based on a test statistic is classified as
19
S IO 0
(A Randomised test
)
2
U S
(B) Non-randomised test
(C) Sequential test
ST
C IS E
(D Bayes test
) T
N
O
62.
M S I
Neyman-Pearson lemma provides
IS
D
(A An unbiased test
) M
A D
(B) A most powerful test
(C) A
An admissible test
(D
N
Minimax test
)
O
M
Equality of several normal populationM
63.
C O means can be tested by
(A Bartlett’s test
)
A T
S
(B) F-test
C U
Page 29
(C) -test
019
(D t -test 2
)
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
019
(D t -test 2
)
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 30
64. If then the correlation between X
and Y is equal to
019
2
(A
)
1
S T
E
T
(B) N
O
SI
IS
(C)
M
M
(D 0
D
)
A
N
O
65. M regression coefficient of the two regression lines is
If one
SA T )
greater
CO (A > 1 O
M than unity, the other will be
CU (B) 1
AT N 19
S IO
(C) < 1
(D 2 0
)
U
C IS S T E ST
N
O
66.
M I
If for two attributes A and B the relation
IS
S holds,
D
the attributes (α )and (β )are
(A Independent M
)
(B)
(C)
(D
N
A
D
Positively associated
Negatively associated
No conclusion
)
M
The c.d.f of a random variable X is M
67.
0x ≤0 C O
{
F ( x )= x 0 < x ≤ 2 π
2π
1 x >2 π
U
S A T
C
and Y is equal to
019
2
(A
)
1
S T
E
T
(B) N
O
SI
IS
(C)
M
M
(D 0
D
)
A
N
O
65. M regression coefficient of the two regression lines is
If one
SA T )
greater
CO (A > 1 O
M than unity, the other will be
CU (B) 1
AT N 19
S IO
(C) < 1
(D 2 0
)
U
C IS S T E ST
N
O
66.
M I
If for two attributes A and B the relation
IS
S holds,
D
the attributes (α )and (β )are
(A Independent M
)
(B)
(C)
(D
N
A
D
Positively associated
Negatively associated
No conclusion
)
M
The c.d.f of a random variable X is M
67.
0x ≤0 C O
{
F ( x )= x 0 < x ≤ 2 π
2π
1 x >2 π
U
S A T
C
Page 31
π π
Then P ( 4
≤X≤
2 )
is equal to
19
20
(A
) S T
E
T
(B)
N
O
(C) SI
IS
M
M
(D
D
) A
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Then P ( 4
≤X≤
2 )
is equal to
19
20
(A
) S T
E
T
(B)
N
O
(C) SI
IS
M
M
(D
D
) A
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 32
68. The Gamma distribution is
(A Positively skewed and leptokurtic 019
) 2
(B) T
Negatively skewed and leptokurtic
S
E
(C) Positively skewed and mesokurtic
(D T
Negatively skewed and mesokurtic
) N
O
S I
69. IS distribution with parameter θ, then
If X follows exponential
M
D
M
− θX
Y =e follow
A
N
(A Gamma distribution
) O
M
M
O
(B) Uniform distribution
CO (D Cauchy distribution
E
(C) Beta distribution
SA T )
C T
CU 70.
AT N
Let X1, X2,…, Xn be a random sample from B(1, p), then the
19
S IO
consistent estimator of is
2 0
U
(A X
)
(B)
C IS S N
T E ST
O
M
X(
(C) )
S I
IS
D
(D n. X
)
M
71. A N
A
D
If a sequence of random variables is convergent in probability
O
then as → ∞ , M
tends to
M
(A
)
1
C O
(B) 0
AT
S
CU
(A Positively skewed and leptokurtic 019
) 2
(B) T
Negatively skewed and leptokurtic
S
E
(C) Positively skewed and mesokurtic
(D T
Negatively skewed and mesokurtic
) N
O
S I
69. IS distribution with parameter θ, then
If X follows exponential
M
D
M
− θX
Y =e follow
A
N
(A Gamma distribution
) O
M
M
O
(B) Uniform distribution
CO (D Cauchy distribution
E
(C) Beta distribution
SA T )
C T
CU 70.
AT N
Let X1, X2,…, Xn be a random sample from B(1, p), then the
19
S IO
consistent estimator of is
2 0
U
(A X
)
(B)
C IS S N
T E ST
O
M
X(
(C) )
S I
IS
D
(D n. X
)
M
71. A N
A
D
If a sequence of random variables is convergent in probability
O
then as → ∞ , M
tends to
M
(A
)
1
C O
(B) 0
AT
S
CU
Page 33
(C)
(D
019
) 2
S T
E
T
72. N
Define the events for a single roll of a die:
O
I
A = {1, 3, 5}; B = {2, 4, 6}; C = {5, 6}. Then
S
S
(A A and B areIdisjoint but not independent
M
) D
M
AB are not disjoint but independent
(B) A and
(C) ANand B are disjoint and independent
(D OA and B are not disjoint and not independent
) M
SA T
73.
CO
M
Given that P(A
O
B) = 5/6, = 1/3 and P ( B́ ) = ½.
T
Then the events A and B are
CU (A
A
Dependent
N 19
S IO
)
(B)
(C)
Independent
Mutually Exclusive 2 0
(D
)
U
C IS S
Conditional events
T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
(D
019
) 2
S T
E
T
72. N
Define the events for a single roll of a die:
O
I
A = {1, 3, 5}; B = {2, 4, 6}; C = {5, 6}. Then
S
S
(A A and B areIdisjoint but not independent
M
) D
M
AB are not disjoint but independent
(B) A and
(C) ANand B are disjoint and independent
(D OA and B are not disjoint and not independent
) M
SA T
73.
CO
M
Given that P(A
O
B) = 5/6, = 1/3 and P ( B́ ) = ½.
T
Then the events A and B are
CU (A
A
Dependent
N 19
S IO
)
(B)
(C)
Independent
Mutually Exclusive 2 0
(D
)
U
C IS S
Conditional events
T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 34
2 2
74. If σ 1 is the error variance of design D1 and σ 2 is the error
19
variance of design D 2 utilizing the same experimental material,
0
the efficiency of D1 over D 2 is 2
1 S T
E
(A σ 21 T
1 N
) O
σ2
2
SI
1 IS
M
(B)
σ 22
A
D
M
1
N
O
σ 21
M
M
O
2 2
(C) σ σ
E
1 2
CO (D
C T
1
AT )
22
σ σ2
1
S
CU
75.
AT N 9
A random variable X takes values 0, 1, 2, 3, ... with probability
1
S IO 2 0
U S T
proportional to . Then P(X ≤ 1) is equal to
S
C IS E
(A 112/125
) T
(B) 110/125
N
O
M I
(C) 113/125
(D 109/125
S
IS
D
)
M
76.
(A
A x
O
N
y
A
e ( e −1 )
D
If e x +e y =e x+ y , then
dy
dx
is
)
y x
e ( e −1 ) M
M
(B)
e y ( e y −1 )
e x ( e x −1 ) C O
y x
e ( e −1 )AT
(C) S
U
x y
e ( e −1 )
C
74. If σ 1 is the error variance of design D1 and σ 2 is the error
19
variance of design D 2 utilizing the same experimental material,
0
the efficiency of D1 over D 2 is 2
1 S T
E
(A σ 21 T
1 N
) O
σ2
2
SI
1 IS
M
(B)
σ 22
A
D
M
1
N
O
σ 21
M
M
O
2 2
(C) σ σ
E
1 2
CO (D
C T
1
AT )
22
σ σ2
1
S
CU
75.
AT N 9
A random variable X takes values 0, 1, 2, 3, ... with probability
1
S IO 2 0
U S T
proportional to . Then P(X ≤ 1) is equal to
S
C IS E
(A 112/125
) T
(B) 110/125
N
O
M I
(C) 113/125
(D 109/125
S
IS
D
)
M
76.
(A
A x
O
N
y
A
e ( e −1 )
D
If e x +e y =e x+ y , then
dy
dx
is
)
y x
e ( e −1 ) M
M
(B)
e y ( e y −1 )
e x ( e x −1 ) C O
y x
e ( e −1 )AT
(C) S
U
x y
e ( e −1 )
C
Page 35
(D e x (1 – e y )
) e y ( e x −1 )
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
) e y ( e x −1 )
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 36
77. Let F(x, y) be the joint p.d.f. of (X, Y). If a, b, c, d are any real
numbers with a < b and 19
, then P[a < X ≤ b, c < Y ≤ d] is
0
equal to 2
(A S T
F(b, d) + F(a, c) – F(b, c) + F(a, d)
E
) T
(B) N
F(b, d) + F(a, c) + F(b, c) + F(a, d)
O
(C)
(D SI
F(b, d) – F(a, c) – F(b, c) + F(a, d)
F(b, d) + F(a, c) – F(b, c) – F(a, d)
) IS
M
A
D
M
78.
N
A discrete r.v. X assumes three values 3, 0, 4 and
P(X = O
M 0) = ½ and E(X) = 9/8. Then is
SA T
O
C )
M
(A 1/8
(B) 2/8
(C) 3/8
O
CU (D
)
1/2
AT N 19
79.
S IO 2 0
A sample study of the people of an area revealed that total
U S T
number of women was 40% and the percentage of coffee
S
drinkers were 45 as a whole and the percentage of male coffee
C IS T E
drinkers was 20. The percentage of female non-coffee drinkers
is
O
N
M I
(A 10
) S
IS
D
(B) 15
(C) 18
M
A D
(D 20
)
A
N
80. O
The arithmetic and geometric mean of two observations are 5
M
and 4 respectively. Then the observations are
M
(A
)
2, 8
C O
(B) 4, 1
AT
(C) 6, 4
S
(D
)
3, 7
CU
numbers with a < b and 19
, then P[a < X ≤ b, c < Y ≤ d] is
0
equal to 2
(A S T
F(b, d) + F(a, c) – F(b, c) + F(a, d)
E
) T
(B) N
F(b, d) + F(a, c) + F(b, c) + F(a, d)
O
(C)
(D SI
F(b, d) – F(a, c) – F(b, c) + F(a, d)
F(b, d) + F(a, c) – F(b, c) – F(a, d)
) IS
M
A
D
M
78.
N
A discrete r.v. X assumes three values 3, 0, 4 and
P(X = O
M 0) = ½ and E(X) = 9/8. Then is
SA T
O
C )
M
(A 1/8
(B) 2/8
(C) 3/8
O
CU (D
)
1/2
AT N 19
79.
S IO 2 0
A sample study of the people of an area revealed that total
U S T
number of women was 40% and the percentage of coffee
S
drinkers were 45 as a whole and the percentage of male coffee
C IS T E
drinkers was 20. The percentage of female non-coffee drinkers
is
O
N
M I
(A 10
) S
IS
D
(B) 15
(C) 18
M
A D
(D 20
)
A
N
80. O
The arithmetic and geometric mean of two observations are 5
M
and 4 respectively. Then the observations are
M
(A
)
2, 8
C O
(B) 4, 1
AT
(C) 6, 4
S
(D
)
3, 7
CU
Page 37
81. The Harmonic mean of 1, 1/2, 1/3, ..., 1/n is 019
2
(A n
S T
E
)
(B) 2n T
(C) 2/(n + 1) N
O
(D n(n + 1)/2
SI
)
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
2
(A n
S T
E
)
(B) 2n T
(C) 2/(n + 1) N
O
(D n(n + 1)/2
SI
)
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 38
82. If arithmetic mean and coefficient of variation of x are 20 and
19
20 respectively, what is the variance of y = 10 2 x?
0
(A 64 2
)
S T
E
(B) 16
(C) 36 T
N
(D 84
O
)
SI
IS
M
83. D
M
If the range of X is 2, what is the range of
A
3X + 50?
(A 2N
) O
M
SAT
CO
M
(B) 6
(C) 44
(D +6
O
CU
)
AT N 19
S IO 0
84. Let X be a r.v. with cumulative distribution function (c.d.f.)
2
F(x). Which one of the following is not the property of c.d.f.?
(A
)
(B)
U
C IS S
Bounded function
T E ST
F is monotonically non decreasing
(C) Point function
N
O
M
(D Right continuous
)
S I
IS
85.
D M
32 factorial experiment means an experiment with
(A
)
(B)
N
A
D
2 factors at 3 levels
3 factors at 2 levels
(C) 3 factors at 3 levels
M
(D 2 factors at 2 levels
M
)
C O
86.
AT
Let X ~ Binomial (2, 1/2) and Y = X2. Then E(Y) is
S
(A 2
CU
19
20 respectively, what is the variance of y = 10 2 x?
0
(A 64 2
)
S T
E
(B) 16
(C) 36 T
N
(D 84
O
)
SI
IS
M
83. D
M
If the range of X is 2, what is the range of
A
3X + 50?
(A 2N
) O
M
SAT
CO
M
(B) 6
(C) 44
(D +6
O
CU
)
AT N 19
S IO 0
84. Let X be a r.v. with cumulative distribution function (c.d.f.)
2
F(x). Which one of the following is not the property of c.d.f.?
(A
)
(B)
U
C IS S
Bounded function
T E ST
F is monotonically non decreasing
(C) Point function
N
O
M
(D Right continuous
)
S I
IS
85.
D M
32 factorial experiment means an experiment with
(A
)
(B)
N
A
D
2 factors at 3 levels
3 factors at 2 levels
(C) 3 factors at 3 levels
M
(D 2 factors at 2 levels
M
)
C O
86.
AT
Let X ~ Binomial (2, 1/2) and Y = X2. Then E(Y) is
S
(A 2
CU
Page 39
)
19
(B) 3/2
(C) 4
(D 1/9 20
)
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
19
(B) 3/2
(C) 4
(D 1/9 20
)
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 40
87. To compare several treatments, when the experimental units are
19
homogeneous, the appropriate design to be used is
0
(A Randomized Block Design 2
)
S T
E
(B) Latin Square Design
(C) Split Plot Design T
N
(D
O
Completely Randomized Design
)
SI
IS
M
88. D
M
A random variable X has mean 50 and variance 100. By using
A
Chebychev’s inequality, the upper bound for P [|X −50|≥ 15 ] is
N
O
(AM 3/ 4
M
O
)
CO (C) 1/9
E
(B) 2/9
SAT (D 4 /9
C T
T
)
CU
A N 19
S IO
dy
89. If y= √ sinx+ √ sinx+ √ sinx … ,then
2 0 dx
is
U S T
(A cos x
S
C IS
) 2 y −1
(B)
sinx x
2 y −1 T E
cos x N
O
M
(C)
y−1
sinx S I
IS
(D
D
) y−1
M
90.
(A
A −1 O
N
A
D
If x √ 1+ y + y √ 1+ x=0 , then
dy
dx
is
) 1+ x M
−1 M
(B)
1+ y
−1 C O
(C)
( 1+ x )2
AT
(D −1 S
) ( 1+ y )2
CU
19
homogeneous, the appropriate design to be used is
0
(A Randomized Block Design 2
)
S T
E
(B) Latin Square Design
(C) Split Plot Design T
N
(D
O
Completely Randomized Design
)
SI
IS
M
88. D
M
A random variable X has mean 50 and variance 100. By using
A
Chebychev’s inequality, the upper bound for P [|X −50|≥ 15 ] is
N
O
(AM 3/ 4
M
O
)
CO (C) 1/9
E
(B) 2/9
SAT (D 4 /9
C T
T
)
CU
A N 19
S IO
dy
89. If y= √ sinx+ √ sinx+ √ sinx … ,then
2 0 dx
is
U S T
(A cos x
S
C IS
) 2 y −1
(B)
sinx x
2 y −1 T E
cos x N
O
M
(C)
y−1
sinx S I
IS
(D
D
) y−1
M
90.
(A
A −1 O
N
A
D
If x √ 1+ y + y √ 1+ x=0 , then
dy
dx
is
) 1+ x M
−1 M
(B)
1+ y
−1 C O
(C)
( 1+ x )2
AT
(D −1 S
) ( 1+ y )2
CU
Page 41
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 42
T T
91. Two contrasts c i ^β and c j ^β are said to be orthogonal if
(A T
c i c j=1 019
) 2
(B) T
c i c j=0 S T
E
(C) c 2i =1 T
(D 2
c j=0 N
O
)
SI
IS
M
M
92. Given the two line of regression as, 3X – 4Y + 8 = 0 and 4X – 3Y
D
A
= 1, the means of X and Y are
N
(A OX =4 ,Y =5
M
O
)
M
SAT
CO (B) X =3 , Y =4
(C)
X =4 /3 ,Y =5/ 4
CU (D
)
AT N
X =3/4 ,Y =4 /5
19
S IO 2 0
93.
U
C IS S E ST
If X and Y are independent with common Exponential
distribution with parameter = 1, then the distribution of
is T
N
O
M
(A A Standard Cauchy distribution
)
S I
IS
D
(B) An Exponential distribution
(C) A Standard Laplace distribution
M
A
(D A Standard Normal distribution
) D
A
N
94. O
The producer’s risk is
M
(A
M
Probability of rejecting a good lot
)
O
Probability of rejecting aC
(B) Probability of accepting a good lot
(C)
T bad lot
SA
(D Probability of accepting a bad lot
)
CU
91. Two contrasts c i ^β and c j ^β are said to be orthogonal if
(A T
c i c j=1 019
) 2
(B) T
c i c j=0 S T
E
(C) c 2i =1 T
(D 2
c j=0 N
O
)
SI
IS
M
M
92. Given the two line of regression as, 3X – 4Y + 8 = 0 and 4X – 3Y
D
A
= 1, the means of X and Y are
N
(A OX =4 ,Y =5
M
O
)
M
SAT
CO (B) X =3 , Y =4
(C)
X =4 /3 ,Y =5/ 4
CU (D
)
AT N
X =3/4 ,Y =4 /5
19
S IO 2 0
93.
U
C IS S E ST
If X and Y are independent with common Exponential
distribution with parameter = 1, then the distribution of
is T
N
O
M
(A A Standard Cauchy distribution
)
S I
IS
D
(B) An Exponential distribution
(C) A Standard Laplace distribution
M
A
(D A Standard Normal distribution
) D
A
N
94. O
The producer’s risk is
M
(A
M
Probability of rejecting a good lot
)
O
Probability of rejecting aC
(B) Probability of accepting a good lot
(C)
T bad lot
SA
(D Probability of accepting a bad lot
)
CU
Page 43
1
95.
2019
The probability density function of X is f ( x )= 4
{ ,∧|x|<2
0 otherwise
.
Then P(2X +3 > 5) is equal to
S T
E
(A 1/3
T
) N
O
(B)
(C)
1/2
1/7 SI
(D 1/4 IS
M
M
)
D
A
N
96. O
Let { X n } be a sequence of random variables. X n converges
M
O
almost surely to X if and only if
M
SAT
CO (A
) n→ ∞
C T
P lim X n=X =0
( )
E
(B) P ( lim X ≠ X ) =a ; 0< a<1
T
n
CU
n→ ∞
N
(C) P ( lim X ≠ X ) =1
A
n
n→ ∞
(D P lim X =X =1
19
S IO
( n
)
) n→ ∞
2 0
97.
U S ST
The relation between almost sure convergence (a.s),
C IS E
convergence in probability (p) and convergence in rth mean (m)
is T
N
O
M I
(A a.s ⟹ m ⟹ p
)
S
IS
D
(B) m ⟹ a.s ⟹ p
(C) a.s ⟹ p; m ⟹ p
M
A D
(D a.s ⟹ p; p ⟹ m
)
A
N
98. O
If Type-I and Type-II errors are kept fixed, then the power of
the test increases, M
Msize
) C O
(A if there is an increase of sample
(B) if sample size remainsTunchanged
S A
(C) if there is a decrease of sample size
CU
(D if the test is unbiased
)
95.
2019
The probability density function of X is f ( x )= 4
{ ,∧|x|<2
0 otherwise
.
Then P(2X +3 > 5) is equal to
S T
E
(A 1/3
T
) N
O
(B)
(C)
1/2
1/7 SI
(D 1/4 IS
M
M
)
D
A
N
96. O
Let { X n } be a sequence of random variables. X n converges
M
O
almost surely to X if and only if
M
SAT
CO (A
) n→ ∞
C T
P lim X n=X =0
( )
E
(B) P ( lim X ≠ X ) =a ; 0< a<1
T
n
CU
n→ ∞
N
(C) P ( lim X ≠ X ) =1
A
n
n→ ∞
(D P lim X =X =1
19
S IO
( n
)
) n→ ∞
2 0
97.
U S ST
The relation between almost sure convergence (a.s),
C IS E
convergence in probability (p) and convergence in rth mean (m)
is T
N
O
M I
(A a.s ⟹ m ⟹ p
)
S
IS
D
(B) m ⟹ a.s ⟹ p
(C) a.s ⟹ p; m ⟹ p
M
A D
(D a.s ⟹ p; p ⟹ m
)
A
N
98. O
If Type-I and Type-II errors are kept fixed, then the power of
the test increases, M
Msize
) C O
(A if there is an increase of sample
(B) if sample size remainsTunchanged
S A
(C) if there is a decrease of sample size
CU
(D if the test is unbiased
)
Page 44
99. 019
A valid t-test to assess an observed difference between two
sample mean value requires 2
S T
E
(i) Both populations are independent
T
(ii) The observations to be sampled from normally distributed
N
parent population O
O 20 SI
(iii) The variance to be the same for both populations
IS
M
D
M
(A (i) and (ii)
) A
(B) Nand (iii)
(ii)
(C) O(i) and (iii)
M All the three conditions
O
(D
M
CO
E
)
SA T
100.
C T
A sufficient condition for an estimator Tn to be consistent for θ
CU is that
(A
AT N
Var (Tn) → 0 as n → ∞
19
S IO 0
)
(B) E (Tn) → θ as n → ∞
2
U S
(C) Var (Tn) /E (Tn) → 0 as n → ∞
(D
ST
E (Tn) → θ and Var (Tn) → 0 as n → ∞
C IS E
)
T
N
101.
O
The arithmetic mean of three sizes 3, 4 and 2.5 weighed
M S I
respectively by the numbers 15, 5 and x is found to be 3. The
IS
D
value of x is
M
A
(A 7
) D
(B) 9 A
(C) 10 N
(D 8 O
) M
M
2
x − x −12 C O
102. lim is
x→ 4 x−4
AT
(A 0 S
)
CU
A valid t-test to assess an observed difference between two
sample mean value requires 2
S T
E
(i) Both populations are independent
T
(ii) The observations to be sampled from normally distributed
N
parent population O
O 20 SI
(iii) The variance to be the same for both populations
IS
M
D
M
(A (i) and (ii)
) A
(B) Nand (iii)
(ii)
(C) O(i) and (iii)
M All the three conditions
O
(D
M
CO
E
)
SA T
100.
C T
A sufficient condition for an estimator Tn to be consistent for θ
CU is that
(A
AT N
Var (Tn) → 0 as n → ∞
19
S IO 0
)
(B) E (Tn) → θ as n → ∞
2
U S
(C) Var (Tn) /E (Tn) → 0 as n → ∞
(D
ST
E (Tn) → θ and Var (Tn) → 0 as n → ∞
C IS E
)
T
N
101.
O
The arithmetic mean of three sizes 3, 4 and 2.5 weighed
M S I
respectively by the numbers 15, 5 and x is found to be 3. The
IS
D
value of x is
M
A
(A 7
) D
(B) 9 A
(C) 10 N
(D 8 O
) M
M
2
x − x −12 C O
102. lim is
x→ 4 x−4
AT
(A 0 S
)
CU
Page 45
(B) ∞
19
(C) 3
(D 7
) 20
S T
E
103. T
The characteristics function of standard Cauchy distribution is
N
O
(A e
−t
SI
)
et
IS
(B)
M
M
D
−|t |
(C) e
(D |t| A
e
) N
O
M
SA T
M
)
O
104. OA design is said to be orthogonal if
C
(A Treatment contrasts are correlated with block contrast
CU
AT
(B) Treatment contrasts are uncorrelated
N
(C) Block contrasts are correlated
9
(D Treatment contrasts are uncorrelated with block contrast
1
S IO 0
)
2
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
19
(C) 3
(D 7
) 20
S T
E
103. T
The characteristics function of standard Cauchy distribution is
N
O
(A e
−t
SI
)
et
IS
(B)
M
M
D
−|t |
(C) e
(D |t| A
e
) N
O
M
SA T
M
)
O
104. OA design is said to be orthogonal if
C
(A Treatment contrasts are correlated with block contrast
CU
AT
(B) Treatment contrasts are uncorrelated
N
(C) Block contrasts are correlated
9
(D Treatment contrasts are uncorrelated with block contrast
1
S IO 0
)
2
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 46
105. Let and are two independent standard normal variates.
19
Then the distribution of 0
2is
(A S T
E
) T
N
(B) N(0, 1) O
SI
(C) IS
M
(D A
D
M
) N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
19
Then the distribution of 0
2is
(A S T
E
) T
N
(B) N(0, 1) O
SI
(C) IS
M
(D A
D
M
) N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 47
106. An unbiased coin is tossed twice. Let X and Y denote the
19
number of times a head turns up and the number of times a tail
0
2
turns up respectively. Pick out the wrong statement from the
alternatives given below
S T
E
(A
T
) N
O
(B) SI
IS
M
M
(C)
D
A
(D
N
) O
M
SA T
CO
107.
M
Let O
be a random sample from
CU
T
distribution, and both are unknown. Define
A N 19
S IO 0
. Which one is not a statistic?
2
U S T
(A
) S
(B) C IS O
N
T E
S I
D
(C)
M
(D
)
N
A
D
M
M
C O
AT
S
CU
19
number of times a head turns up and the number of times a tail
0
2
turns up respectively. Pick out the wrong statement from the
alternatives given below
S T
E
(A
T
) N
O
(B) SI
IS
M
M
(C)
D
A
(D
N
) O
M
SA T
CO
107.
M
Let O
be a random sample from
CU
T
distribution, and both are unknown. Define
A N 19
S IO 0
. Which one is not a statistic?
2
U S T
(A
) S
(B) C IS O
N
T E
S I
D
(C)
M
(D
)
N
A
D
M
M
C O
AT
S
CU
Page 48
108. Let be a random sample from a normal
019
2
S T
E
distribution having the variance 4. Let and
T
N
O
SI the value of E(S) is
. Then
IS
M
M
(A 22
) D
(B) 44 A
(C) 25N
(D O
M 40
M
O
)
SA T
CO
109.
If the regression line of Y on X is Y = 23 – 2.0X and the
T
coefficient of determination is 0.49, the coefficient of
CU
N
correlation is
(A
)
(B)
A
S IO
0.49
0.70 2 0 19
(C)
(D
) U
C IS S
-0.70
-0.49
T E ST
N
O
M I
110. If the if x = 0 and if x = 1,
S
IS
D
what will be the
M
A
(A 0
) D
(B) 1 A
(C) 1/2 N
(D 2/3 O
) M
M
C O
111. If a statistic t follows Student’s t distribution with digress of
freedom n, then t follows T
2
S
(A Student’s t-distribution
A with n degrees of freedom
2
)
CU
019
2
S T
E
distribution having the variance 4. Let and
T
N
O
SI the value of E(S) is
. Then
IS
M
M
(A 22
) D
(B) 44 A
(C) 25N
(D O
M 40
M
O
)
SA T
CO
109.
If the regression line of Y on X is Y = 23 – 2.0X and the
T
coefficient of determination is 0.49, the coefficient of
CU
N
correlation is
(A
)
(B)
A
S IO
0.49
0.70 2 0 19
(C)
(D
) U
C IS S
-0.70
-0.49
T E ST
N
O
M I
110. If the if x = 0 and if x = 1,
S
IS
D
what will be the
M
A
(A 0
) D
(B) 1 A
(C) 1/2 N
(D 2/3 O
) M
M
C O
111. If a statistic t follows Student’s t distribution with digress of
freedom n, then t follows T
2
S
(A Student’s t-distribution
A with n degrees of freedom
2
)
CU
Page 49
(B) Snedecor’s F-distribution with (1, n) degrees of freedom
19
(C) Snedecor’s F-distribution with (n, 1) degrees of freedom
(D None of the above
) 20
S T
E
112. T
The number of non-negative variables in a basic feasible
N
solution to a
O
transportation problem is:
SI
(A mn
IS
M
M
)
(B) m+n D
(C) m+n+1A
(D N
None of the above
) O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
19
(C) Snedecor’s F-distribution with (n, 1) degrees of freedom
(D None of the above
) 20
S T
E
112. T
The number of non-negative variables in a basic feasible
N
solution to a
O
transportation problem is:
SI
(A mn
IS
M
M
)
(B) m+n D
(C) m+n+1A
(D N
None of the above
) O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 50
113. Which of the following statements about confidence intervals is
INCORRECT?
0 19
(A If we keep the sample size fixed, 2 the confidence interval
)
S Tconfidence coefficient
gets wider as we increase the
(B) A confidence interval forEa mean always contains the
sample mean T
N coefficient fixed, the
O
(C) If we keep the confidence
SI gets narrower as we increase the
confidence interval
sample sizeIS
Mintervalstandard
M
(D If the population deviation increases, the
) D
confidence decreases in width
A
N
O
114. If a primal LP problem has a finite solution, then the dual LP
M
M should have
O
problem
SA
CO (A finite solution
T )
T
(B) infeasible solution
CU
N
(C) unbounded solution
A
(D None of the above
19
S IO
)
2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
INCORRECT?
0 19
(A If we keep the sample size fixed, 2 the confidence interval
)
S Tconfidence coefficient
gets wider as we increase the
(B) A confidence interval forEa mean always contains the
sample mean T
N coefficient fixed, the
O
(C) If we keep the confidence
SI gets narrower as we increase the
confidence interval
sample sizeIS
Mintervalstandard
M
(D If the population deviation increases, the
) D
confidence decreases in width
A
N
O
114. If a primal LP problem has a finite solution, then the dual LP
M
M should have
O
problem
SA
CO (A finite solution
T )
T
(B) infeasible solution
CU
N
(C) unbounded solution
A
(D None of the above
19
S IO
)
2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 51
115. The dual of the primal maximization LP problem having m
19
constraints and n non-negative variables should
0
2 variables
(A have n constraints and m non-negative
)
S T
TE
(B) be a minimization LP problem
(C) both (A) and (B)
(D None of the above N
O
)
S I
IS
M
D
M
116. Consider the statements:
A
I.N Maximum likelihood estimators are always
O unbiased.
M
T
CO
O
M II. Maximum likelihood estimators are always
C T
unique.
E
SA Which of the statements given above is/are correct?
CU (A
)
AT
I only
N 19
S IO 0
(B) II only
(C) Both I and II 2
U S T
(D Neither I nor II
)
S
117. C IS N
T E
Suppose X is a random variable taking values +1 and -1 only
O
M I
with probability c/3 and c/6 respectively. Let Y = X2. Then
S
IS
D
(A c=1 and P(Y=0)=1
)
M
A
(B) c=1 and P(Y=1)=1
(C) D
c=2 and P(Y=1)=1
(D A
c=2 and P(Y=0)=1
) N
O
M
118.
M
A sampling technique in which only the first unit is selected
C O
with the help of random numbers and the rest get selected
automatically according to some pre-designed pattern is known
as
A T
(A stratified randomSsampling
)
CU
19
constraints and n non-negative variables should
0
2 variables
(A have n constraints and m non-negative
)
S T
TE
(B) be a minimization LP problem
(C) both (A) and (B)
(D None of the above N
O
)
S I
IS
M
D
M
116. Consider the statements:
A
I.N Maximum likelihood estimators are always
O unbiased.
M
T
CO
O
M II. Maximum likelihood estimators are always
C T
unique.
E
SA Which of the statements given above is/are correct?
CU (A
)
AT
I only
N 19
S IO 0
(B) II only
(C) Both I and II 2
U S T
(D Neither I nor II
)
S
117. C IS N
T E
Suppose X is a random variable taking values +1 and -1 only
O
M I
with probability c/3 and c/6 respectively. Let Y = X2. Then
S
IS
D
(A c=1 and P(Y=0)=1
)
M
A
(B) c=1 and P(Y=1)=1
(C) D
c=2 and P(Y=1)=1
(D A
c=2 and P(Y=0)=1
) N
O
M
118.
M
A sampling technique in which only the first unit is selected
C O
with the help of random numbers and the rest get selected
automatically according to some pre-designed pattern is known
as
A T
(A stratified randomSsampling
)
CU
Page 52
(B) multi-stage sampling
19
(C) cluster sampling
(D systematic sampling
) 20
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
19
(C) cluster sampling
(D systematic sampling
) 20
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 53
119. Normal distribution is also known as
(A Gaussian distribution 019
) 2
(B) Poisson distribution
S T
E
(C) Bernoulli’s distribution
(D T
Weighted average distribution
) N
O
S I
IS distribution, if value of is integer, then
120. In Poisson probability
M
D be
distribution will
A
M
N
(A bimodal
) O
M
O
(B) unimodal
M
CO (D negative modal
E
(C) positive modal
SA T )
C T
CU 121.
AT N
Method in which previously calculated probabilities are revised
9
with new probabilities using other available information is
1
based on
S IO 2 0
U S T
(A updating theorem
) S
C IS E
(B) revised theorem
(C) Bayes theorem T
(D dependency theorem N
O
M I
)
S
IS
122.
D
If two events X and Y are considered as partially overlapping
M
A D
events, then rule of addition can be written as
(A A
P(X or Y) = P(X) – P(Y) + P(X and Y)
) N
(B) O
P(X or Y) = P(X) + P(Y) * P(X – Y)
(C) M
P(X or Y) = P(X) * P(Y) + P(X – Y)
(D M
P(X or Y) = P(X) + P(Y) – P(X and Y)
)
C O
A T
S
123. If U
C then the value of e is
(A Gaussian distribution 019
) 2
(B) Poisson distribution
S T
E
(C) Bernoulli’s distribution
(D T
Weighted average distribution
) N
O
S I
IS distribution, if value of is integer, then
120. In Poisson probability
M
D be
distribution will
A
M
N
(A bimodal
) O
M
O
(B) unimodal
M
CO (D negative modal
E
(C) positive modal
SA T )
C T
CU 121.
AT N
Method in which previously calculated probabilities are revised
9
with new probabilities using other available information is
1
based on
S IO 2 0
U S T
(A updating theorem
) S
C IS E
(B) revised theorem
(C) Bayes theorem T
(D dependency theorem N
O
M I
)
S
IS
122.
D
If two events X and Y are considered as partially overlapping
M
A D
events, then rule of addition can be written as
(A A
P(X or Y) = P(X) – P(Y) + P(X and Y)
) N
(B) O
P(X or Y) = P(X) + P(Y) * P(X – Y)
(C) M
P(X or Y) = P(X) * P(Y) + P(X – Y)
(D M
P(X or Y) = P(X) + P(Y) – P(X and Y)
)
C O
A T
S
123. If U
C then the value of e is
Page 54
(A 2.71828
19
)
(B)
(C)
2.81928
2.91728 20
(D 2.71928
S T
E
)
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
19
)
(B)
(C)
2.81928
2.91728 20
(D 2.71928
S T
E
)
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 55
124. The polynomial equation of the least degree having -1, 1, 2 and
3 as roots is
019
(A 4 3
x −5 x + 5 x −6=0 2
) S T
E
(B) 4 3 2
x −5 x + 5 x +5 x −5=0 T
N
O
(C) x −5 x + 5 x +5Ix − 6=0
SS
4 3 2
I
(D x −5 x −M5 x +5 x − 6=0
M
4 3 2
) D
A
N
O
M
SA
T
O
M
C (for all i and j )
(A
O
125. A complex square matrix
is said to be Hermitian matrix if
CU )
AT N 19
S IO
(B)
2 0
U S
(C)
ST
C IS E
(D
) T
N
O
126.
S I
If A is orthogonal, then | A| is
D M
A D
(A +1
) A
N
(B)
O
(C) ± 1 M
M
(D
)
0
C O
AT
S
127.
C U
is equal to
3 as roots is
019
(A 4 3
x −5 x + 5 x −6=0 2
) S T
E
(B) 4 3 2
x −5 x + 5 x +5 x −5=0 T
N
O
(C) x −5 x + 5 x +5Ix − 6=0
SS
4 3 2
I
(D x −5 x −M5 x +5 x − 6=0
M
4 3 2
) D
A
N
O
M
SA
T
O
M
C (for all i and j )
(A
O
125. A complex square matrix
is said to be Hermitian matrix if
CU )
AT N 19
S IO
(B)
2 0
U S
(C)
ST
C IS E
(D
) T
N
O
126.
S I
If A is orthogonal, then | A| is
D M
A D
(A +1
) A
N
(B)
O
(C) ± 1 M
M
(D
)
0
C O
AT
S
127.
C U
is equal to
Page 56
(A 2
19
)
(B)
(C)
0
1 20
(D 4
S T
E
)
T
N
O
128. Γ ( n+1) is equal to
SI
n! IS
(A
M
)
A
D
M
N
(B) (n+1) !
O
(C)M Γn
SAT
M
CO (D
)
(n −1)!
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
19
)
(B)
(C)
0
1 20
(D 4
S T
E
)
T
N
O
128. Γ ( n+1) is equal to
SI
n! IS
(A
M
)
A
D
M
N
(B) (n+1) !
O
(C)M Γn
SAT
M
CO (D
)
(n −1)!
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 57
129. Histogram can be used only when
(A Class intervals are equal or unequal019
) 2
(B) Class intervals are all equal
S T
E
(C) Class intervals are unequal
(D T
Frequencies in class interval are equal
) N
O
S I
ISbivariate N(0,0,1,1, ρ), then the variables X
130. If (X, Y) follows the
M
+ Y and X – Y
A
Dare
M
N
(A Correlated with ρ = ½
) O
M
SA
M
O E
CO (C) Negatively correlated
(B) Independently distributed
C T
T (D None of the above
T
)
CU
131.
A N
Bias of an estimator can be
19
(A
S IO
Positive
2 0
U S
)
(B) Negative
ST
C IS E
(C) Either positive or negative
(D Always zero T
)
N
O
132.
S I
Range of the variance ratio F is
(A
D to 1 M
)
(B) A to
O
N
A
D
(C) 0 to
M
(D 0 to 1 M
)
C O
AT
133.
S
If each value X is divided by 2 and Y is multiplied by 2, then
C U
by coded values is
(A Class intervals are equal or unequal019
) 2
(B) Class intervals are all equal
S T
E
(C) Class intervals are unequal
(D T
Frequencies in class interval are equal
) N
O
S I
ISbivariate N(0,0,1,1, ρ), then the variables X
130. If (X, Y) follows the
M
+ Y and X – Y
A
Dare
M
N
(A Correlated with ρ = ½
) O
M
SA
M
O E
CO (C) Negatively correlated
(B) Independently distributed
C T
T (D None of the above
T
)
CU
131.
A N
Bias of an estimator can be
19
(A
S IO
Positive
2 0
U S
)
(B) Negative
ST
C IS E
(C) Either positive or negative
(D Always zero T
)
N
O
132.
S I
Range of the variance ratio F is
(A
D to 1 M
)
(B) A to
O
N
A
D
(C) 0 to
M
(D 0 to 1 M
)
C O
AT
133.
S
If each value X is divided by 2 and Y is multiplied by 2, then
C U
by coded values is
Page 58
(A
Same as
)
019
(B) Twice of
2
S T
E
(C) Four times of T
N
O
(D
Eight times of S
I
)
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Same as
)
019
(B) Twice of
2
S T
E
(C) Four times of T
N
O
(D
Eight times of S
I
)
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 59
134. If the index number is independent of the units of measurement,
then it satisfies
019
(A Time reversal test 2
)
S T
E
(B) Factor reversal test
(C) Unit test T
N
(D All of the above
O
)
SI
IS
M
135. D
M
Variation due to assignable causes in the product occurs due to
A
(A N process
Faulty
) O
M
M Carelessness
O
(B) of operators
CO
E
(C)Poor quality of raw material
C T
(D All of the above
AT )
S
CU 136.
AT N
Missing observation in a CRD is to be
19
S IO 0
(A Estimated
)
2
U S
(B) Deleted
(C) Guessed
ST
C IS E
(D None of the above
) T
N
O
137.
M S I
If two events A and B are such that A ⊂ B and B⊂ A , the
IS
D
relation between P(A) and P(B) is
(A P( A)≤ P( B) M
)
(B) A O
N
P( A)≥ P(B)
A
D
(C) P( A)=P(B)
M
M
(D
)
None of the above
C O
AT
138.
S
The moment generating function of the Bernoulli distribution is
CU
then it satisfies
019
(A Time reversal test 2
)
S T
E
(B) Factor reversal test
(C) Unit test T
N
(D All of the above
O
)
SI
IS
M
135. D
M
Variation due to assignable causes in the product occurs due to
A
(A N process
Faulty
) O
M
M Carelessness
O
(B) of operators
CO
E
(C)Poor quality of raw material
C T
(D All of the above
AT )
S
CU 136.
AT N
Missing observation in a CRD is to be
19
S IO 0
(A Estimated
)
2
U S
(B) Deleted
(C) Guessed
ST
C IS E
(D None of the above
) T
N
O
137.
M S I
If two events A and B are such that A ⊂ B and B⊂ A , the
IS
D
relation between P(A) and P(B) is
(A P( A)≤ P( B) M
)
(B) A O
N
P( A)≥ P(B)
A
D
(C) P( A)=P(B)
M
M
(D
)
None of the above
C O
AT
138.
S
The moment generating function of the Bernoulli distribution is
CU
Page 60
(A
)
019
(B) 2
S T
E
(C) T
N
O
(D
SI
IS
)
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
)
019
(B) 2
S T
E
(C) T
N
O
(D
SI
IS
)
M
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 61
139. The degrees of freedom for students- t based on a random
sample of size n is
019
(A n −1 2
) S T
E
(B) n T
N
O
(C) (n −2)
SI
n −1 IS
(D
M
) 2
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
sample of size n is
019
(A n −1 2
) S T
E
(B) n T
N
O
(C) (n −2)
SI
n −1 IS
(D
M
) 2
A
D
M
N
O
M
SAT
CO
M
O
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 62
140. If X ~ b (n , p1 ) and the sum of the variates
( X 1 + X 2) is distributed as
019
2
(A Hypergeometric distribution
S T
)
E
(B) Binomial distribution T
(C) Poisson distributionN
O
(D None of the above
SI
IS
)
M
D
M
A ). Then the central moments of odd order are
141. Let
N
O
(A One
M
M
O
)
CO (C) Infinite
E
(B) Zero
SAT (D
C T
Positive
T
)
CU
142.
A N 9
If we have a sample size n from a population of N units, the
1
S IO
finite population correction is
2 0
U S T
(A N −1
S
C IS
) N
n −1 T E
(B)
N N
O
(C)
M
N −n
IS
S I
D
N
M
A D
(D N −n
) n
A
N
O
143. M
For a random sample from a Poisson population the
M
maximum likelihood estimate of λ is
C O
(A Median
)
AT
(B) Mode
S
(C) Geometric mean
CU
( X 1 + X 2) is distributed as
019
2
(A Hypergeometric distribution
S T
)
E
(B) Binomial distribution T
(C) Poisson distributionN
O
(D None of the above
SI
IS
)
M
D
M
A ). Then the central moments of odd order are
141. Let
N
O
(A One
M
M
O
)
CO (C) Infinite
E
(B) Zero
SAT (D
C T
Positive
T
)
CU
142.
A N 9
If we have a sample size n from a population of N units, the
1
S IO
finite population correction is
2 0
U S T
(A N −1
S
C IS
) N
n −1 T E
(B)
N N
O
(C)
M
N −n
IS
S I
D
N
M
A D
(D N −n
) n
A
N
O
143. M
For a random sample from a Poisson population the
M
maximum likelihood estimate of λ is
C O
(A Median
)
AT
(B) Mode
S
(C) Geometric mean
CU
Page 63
(D Mean
19
)
20
144. Analysis of variance utilizes
S T
E
(A F -test T
) N
O
SI
IS
2
(B) χ -test
M
(C) Z-test
A
D
M
N
(D t -test
) O
M
SA T
CO
145.
M
If
O
C T E then the value of correlation
T
coefficient r XYis
CU (A 0
A N 19
S IO
)
(B) 1 2 0
(C)
(D
U
C IS
0.5
S T E ST
) N
O
S I
D
146. If X is Uniform over (a, b) and if (α, β) is a sub interval of (a,
M
b), then P(α < X < β) is equal to
(A
) A β−α
b−a
α−β O
N
A
D
(B)
b−a M
α−β M
(C)
( b −a )2
C O
(D α+β
AT
) ( a −b )2
S
CU
19
)
20
144. Analysis of variance utilizes
S T
E
(A F -test T
) N
O
SI
IS
2
(B) χ -test
M
(C) Z-test
A
D
M
N
(D t -test
) O
M
SA T
CO
145.
M
If
O
C T E then the value of correlation
T
coefficient r XYis
CU (A 0
A N 19
S IO
)
(B) 1 2 0
(C)
(D
U
C IS
0.5
S T E ST
) N
O
S I
D
146. If X is Uniform over (a, b) and if (α, β) is a sub interval of (a,
M
b), then P(α < X < β) is equal to
(A
) A β−α
b−a
α−β O
N
A
D
(B)
b−a M
α−β M
(C)
( b −a )2
C O
(D α+β
AT
) ( a −b )2
S
CU
Page 64
147. Let X be a random variable (r.v.). Then Y = 1/X is also a
(A Random variable 019
) 2
(B) T
Random variable provided P(X = 0) = 0
S
E
(C) Random variable provided P(X =0) = 1
(D Not a Random variable T
) N
O
SI
S
148. If the values of theI1 and 3 quartiles are 20 and 30
st rd
M
respectively, then
A
M
D the value of inter quartile range is
(A 10N
) O
M
O
(B) 25
M
CO (D 0
E
(C) 5
SA T )
C T
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
(A Random variable 019
) 2
(B) T
Random variable provided P(X = 0) = 0
S
E
(C) Random variable provided P(X =0) = 1
(D Not a Random variable T
) N
O
SI
S
148. If the values of theI1 and 3 quartiles are 20 and 30
st rd
M
respectively, then
A
M
D the value of inter quartile range is
(A 10N
) O
M
O
(B) 25
M
CO (D 0
E
(C) 5
SA T )
C T
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 65
149. Let { A n } be a sequence of independent events, P , if
(A ∑ P ( A n|) <∞ 019
) 2
(B) ∑ P ( A n|)=∞ S T
E
(C) ∑ P ( A n|)=1 T
(D ∑ P ( A n|) <1 N
O
)
SI
IS
M
M
150. If Tn is unbiased and consistent for θ, then
D
(A T isAunbiased and consistent for θ
2 2
N n
) O
(B)M T is unbiased but not consistent for θ
2 2
O
n
M 2
(C) T is biased but consistent for θ 2
CO (D
E
n
Tn is biased and not consistent for θ2
2
SAT )
C T
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
(A ∑ P ( A n|) <∞ 019
) 2
(B) ∑ P ( A n|)=∞ S T
E
(C) ∑ P ( A n|)=1 T
(D ∑ P ( A n|) <1 N
O
)
SI
IS
M
M
150. If Tn is unbiased and consistent for θ, then
D
(A T isAunbiased and consistent for θ
2 2
N n
) O
(B)M T is unbiased but not consistent for θ
2 2
O
n
M 2
(C) T is biased but consistent for θ 2
CO (D
E
n
Tn is biased and not consistent for θ2
2
SAT )
C T
CU
AT N 19
S IO 2 0
U
C IS S T E ST
N
O
S I
D M
N
A
D
M
M
C O
AT
S
CU
Page 66
STATISTICS 9 - ANSWER KEY
1
20 CODE: 614
TEST
QN. NO. KEY QN. NO. KEY QN. NO. T KEY QN. NO. KEY QN. NO. KEY
E S
1 C 26 D 51 T B 76 A 101 C
2 C 27 C N
O52 B 77 B 102 D
3 C 28 C I
S 53 D 78 C 103 C
4 D 29 B IS 54 D 79 B 104 D
M
5 B 30 C AD 55
M C 80 A 105 A
6 C 31 DN 56 B 81 C 106 A
O
7 A 32 MB 57 C 82 A 107 A
8
9
10
A
D
B
33
34 T
S
35A
CO
M C
C
D
O
C TE
58
59
60
A
A
B
83
84
85
D
C
A
108
109
110
D
C
A
11
12
B
C
CU36
37
B
A
AT N
61
62
B
B
86
87
19
B
D
111
112
B
D
13 C 38 A
S I O 63 B
2 0
88 D 113 D
U S
14 B 39 A 64 D 89 A 114 A
15 B 40 B 65 C ST 90 C 115 C
16
17
C
B
41
42 C IS
C
A
66
67
O
N
A
B
T E 91
92
B
A
116
117
D
C
18 D 43
M
C 68
IS
S I A 93 C 118 D
D
19 B 44 D 69 B 94 A 119 A
20 C 45 B 70M C 95 D 120 A
21
22
23
C
D
A
46
47
48
A B
B
B O
N
A
D
71
72
73
A
A
B
96
97
98
C
C
A
121
122
123
C
D
A
M
24 C 49 C 74
M A 99 D 124 C
CO
25 D 50 A 75 A 100 D 125 C
AT
S
CU
1
20 CODE: 614
TEST
QN. NO. KEY QN. NO. KEY QN. NO. T KEY QN. NO. KEY QN. NO. KEY
E S
1 C 26 D 51 T B 76 A 101 C
2 C 27 C N
O52 B 77 B 102 D
3 C 28 C I
S 53 D 78 C 103 C
4 D 29 B IS 54 D 79 B 104 D
M
5 B 30 C AD 55
M C 80 A 105 A
6 C 31 DN 56 B 81 C 106 A
O
7 A 32 MB 57 C 82 A 107 A
8
9
10
A
D
B
33
34 T
S
35A
CO
M C
C
D
O
C TE
58
59
60
A
A
B
83
84
85
D
C
A
108
109
110
D
C
A
11
12
B
C
CU36
37
B
A
AT N
61
62
B
B
86
87
19
B
D
111
112
B
D
13 C 38 A
S I O 63 B
2 0
88 D 113 D
U S
14 B 39 A 64 D 89 A 114 A
15 B 40 B 65 C ST 90 C 115 C
16
17
C
B
41
42 C IS
C
A
66
67
O
N
A
B
T E 91
92
B
A
116
117
D
C
18 D 43
M
C 68
IS
S I A 93 C 118 D
D
19 B 44 D 69 B 94 A 119 A
20 C 45 B 70M C 95 D 120 A
21
22
23
C
D
A
46
47
48
A B
B
B O
N
A
D
71
72
73
A
A
B
96
97
98
C
C
A
121
122
123
C
D
A
M
24 C 49 C 74
M A 99 D 124 C
CO
25 D 50 A 75 A 100 D 125 C
AT
S
CU
Page 67
019
2
QN. NO. KEY
S T
TE
126 C
127 D N
O
128 A SI
129 B IS
M
130 B A
D
M
131 C N
O
132 C M
133
134
135
C
C
D SA
T
CO
M
O
C TE
136
137
B
C
CU
AT N 19
138 C
S I O 2 0
U S
139 A
140 B ST
141
142
B
C C IS O
N
T E
143 D
M IS
S I
D
144 A
145 A M
146
147
148
A
B
C
A O
N
A
D
M
149 A
M
CO
150 C
AT
S
CU
2
QN. NO. KEY
S T
TE
126 C
127 D N
O
128 A SI
129 B IS
M
130 B A
D
M
131 C N
O
132 C M
133
134
135
C
C
D SA
T
CO
M
O
C TE
136
137
B
C
CU
AT N 19
138 C
S I O 2 0
U S
139 A
140 B ST
141
142
B
C C IS O
N
T E
143 D
M IS
S I
D
144 A
145 A M
146
147
148
A
B
C
A O
N
A
D
M
149 A
M
CO
150 C
AT
S
CU
Document Details
| Board / Org | Cochin University |
| Exam | CUSAT CAT |
| Type | Question Paper |
| Pages | 67 |
| Updated | 30 Apr 2026 |