MBOSE Class 12 Question Paper 2024 for Statistics

Meghalaya Board of School Education

QUESTION
PAPERS

Total No. of Printed Pages—8
HS/XII/A. Sc/S/24

2024

STATISTICS

Full Marks : 100

Time : 3 hours

The figures in the margin indicate full marks for the questions

General Instructions :
(i) Write all the answers in the Answer Script.
(ii) Attempt Part—A (Objective Questions) serially.
(iii) Attempt all parts of a question together at one place.

( PART : A—OBJECTIVE )
( Marks : 50 )

SECTION—I
( Marks : 20 )

1. Choose and write the correct answer : 1×10=10
9
(a) If E (X ) = , then the value of E (2X + 1) is
2
9
(i)
2
11
(ii)
2
(iii) 10
(iv) 9

/22 [ P.T.O.

( 2 )

(b) A Poisson distribution is

(i) uni-parametric

(ii) bi-parametric

(iii) tri-parametric

(iv) None of the above

(c) The standard deviation of a binomial distribution is
(i) npq

(ii) npq
(iii) np

(iv) None of the above

(d) Var(X ) is equal to
(i) { E (X )} 2 - E (X )2
(ii) E (X )2 - { E (X )} 2
(iii) { E (X )} 2
(iv) E (X )2

(e) In a given business venture, a man can make a profit
of R 1,000 with a probability of 0·8 or take a loss of
R 400 with a probability of 0·2. Then the expectation
is
(i) R 270
(ii) R 720
(iii) R 40,000
(iv) None of the above

HS/XII/A. Sc/S/24/22 [ Contd.

( 3 )

å p 1q 0
(f) The index number is given by
å p 0q 0

(i) Laspeyres’ formula
(ii) Fisher’s formula
(iii) Paasche’s formula
(iv) Marshall-Edgeworth formula

(g) Base period for an index number should be
(i) a year only
(ii) a normal period
(iii) a period at distant past
(iv) None of the above

(h) Changes that take place as a result of natural
calamities are classified under the head
(i) secular movement
(ii) seasonal variation
(iii) cyclical variation
(iv) irregular variation

(i) The number of possible samples of size n out of
population of size N without replacement is
N
(i) Cn

(ii) ( N )n

(iii) n 2

(iv) n !

HS/XII/A. Sc/S/24/22 [ P.T.O.

( 4 )

(j) A sample consists of
(i) all units of population
(ii) 50% unit of population
(iii) 5% unit of population
(iv) any fraction of population

2. Fill in the blanks : 1×5=5

(a) If x i is a random variable with probability f (x i ), then
its expectation is _____.

(b) The expected value of the number X shown on the
face when a die is thrown is _____.

(c) For a binomial distribution given by b (x,10, 0 × 4), the
mean is _____.

(d) Time series consists of _____ components.

(e) In simple random sampling, _____ is an unbiased
estimate of population mean.

3. Write whether the following statements are True or False :
1×5=5

(a) Mean < variance is a binomial distribution.

(b) The expected value of a constant is a constant itself.

(c) The standard normal distribution is denoted by
N (0,1.
)

(d) Trend is attached to short-term fluctuation.

(e) In SRSWR, the same sampling unit may occur more
than once.

HS/XII/A. Sc/S/24/22 [ Contd.

( 5 )

SECTION—II
( Marks : 30 )

4. Answer the following questions : 3×10=30

(a) If X and Y are independent random variables, then
show that E[{ X - E (X )} {Y - E (Y )}] = 0.

(b) Suppose 8% of the people are left-handed. What is
the probability that 2 or more of a random sample of
25 are left-handed? (Given e -2 = 0 ×135)

(c) In tossing two coins, let X be the number of heads
shown. Find E (X ) and E (X -1)2 .

(d) The mean and variance of a binomial distribution are
4 and 4/3 respectively. Find P (X ³ 1.
)

(e) 10 eggs are drawn successively from a lot containing
10% defective eggs. Find the probability that there is
at least one defective egg.

(f) Discuss the uses of index number.

(g) Distinguish between seasonal and cyclical variation.

(h) Show that in SRSWOR, the sample mean is an
unbiased estimate of population mean.

(i) What do you mean by ‘family budget enquiry’?

(j) Why is index number called an ‘economic barometer’?

HS/XII/A. Sc/S/24/22 [ P.T.O.

( 6 )

( PART : B—DESCRIPTIVE )
( Marks : 50 )

Answer four questions, taking at least one from each Group

GROUP—A

5. (a) Define mathematical expectation of a random
variable.
If X and Y are two independent random variates, then
prove that E (XY ) = E (X ) E (Y ). 2+4=6

(b) What is Bernoulli’s trial? In a series of n Bernoulli’s
trial with constant probability of success p and
failure q, q = 1 - p, obtain the probability of X
success. 1½+3=4½
(c) Prove that
E[(X - C )2 ] = Var(X ) + [E (X ) - C ]2
where C is a constant. 2

6. (a) In a college, there are 500 students, 40% students
are girls. 10 students are selected at random. X
denotes the number of girls among the selected
students. Find the value of P (X = 4). 4

(b) State under what condition Poisson distribution can
be obtained from Binomial distribution. 1½

(c) If X follows Poisson distribution and

P (X = 0) = P (X = 1) = a
1
then show that a = . 3
e

HS/XII/A. Sc/S/24/22 [ Contd.

( 7 )

(d) The number of mistakes counted in a 100 typed
pages, of a typist revealed that he made 2·8 mistakes
on an average per page. Find the probability that in a
page typed by him :

(i) There is no mistake

(ii) There are two or more mistakes
(Given e -2× 8 = 0 × 061) 4

GROUP—B

7. (a) What are the components of a time series? Discuss
each of them citing suitable examples. 1½+5=6½

(b) Find a 3-year moving average from the following
data : 2

Year 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939
Index No. 158 147 144 140 141 143 147 154 156 158

(c) Discuss the advantages of the method of moving
average in measuring trend. 4

8. (a) Write a note on the choice of the base year in the
construction of index number. 4

(b) Explain the time reversal and factor reversal tests of
an index number. Show that Fisher’s index number
satisfies both the tests of an index number. 2+4=6

(c) What is the cost of living index number? 2½

HS/XII/A. Sc/S/24/22 [ P.T.O.

( 8 )

GROUP—C

9. (a) Discuss the advantages of sampling over complete
enumeration. 6½

(b) What is stratified random sampling? Discuss the
advantages of stratified random sampling over simple
random sampling. 2+4=6

10. (a) Write a brief note on the errors that creep up in
sample survey. 6½

(b) Write short notes on the following : 2+2+2=6

(i) Parameter

(ii) Statistic

(iii) Pilot survey

HHH

HS/XII/A. Sc/S/24/22 24K—100

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