MBOSE Class 12 Question Paper 2018 for Statistics

Total No. of Printed Pages—11
HS/XII/A. Sc/S/18

2018

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
(a) If n = 25, p = 2 and q = 3, then the standard
5 5
deviation of the binomial distribution is

(i) 6

(ii) 6

(iii) 5

(iv) 10

/46

( 2 )

(b) The equality of mean and variance of a discrete
distribution indicates that the distribution is

(i) Poisson

(ii) binomial

(iii) normal

(iv) hypergeometric

(c) If E (2X + 3) = 27, then the value of E (X ) is

(i) 12

(ii) 9
2

(iii) 5

(iv) 7

(d) The mean of a binomial distribution is 27 and
q = 1, then the variance is
3

(i) 81

(ii) 3

(iii) 9

(iv) 80
3

( 3 )

(e) In a given business venture, a man can make
a profit of R 1,000 with probability 0·8 or take
a loss of R 400 with probability 0·2, then the
expectation is

(i) R 270

(ii) R 720

(iii) R 40,000

(iv) None of the above

(f) The price indices Laspeyres’, Paasche’s and
Fisher’s are related by which of the following
inequalities?

(i) Laspeyres ³ Fisher ³ Paasche

(ii) Laspeyres £ Fisher £ Paasche

(iii) Fisher ³ Laspeyres ³ Paasche

(iv) Paasche ³ Laspeyres ³ Fisher

(g) A binomial distribution is

(i) uniparametric

(ii) biparametric

(iii) triparametric

(iv) None of the above

( 4 )

(h) Changes that take place as a result of natural
calamities are classified under the head

(i) secular movement

(ii) seasonal variations

(iii) cyclical variations

(iv) irregular variations

(i) Which of the following is not a method for
measuring trend?

(i) Graphic method

(ii) Moving-average method

(iii) Harmonic-analysis method

(iv) Least-squares method

(j) The most important factor(s) causing seasonal
variations is/are

(i) growth of population

(ii) depression in business

(iii) weather and social customs

(iv) None of the above

( 5 )

2. Fill in the blanks : 1×5=5

(a) The term ‘parameter’ is used to denote the
characteristic of the _____.

(b) If m be the expected value of x, then
E (x - m) = _____.

(c) Fisher’s index number is called _____ index
number.

(d) Normal distribution is a _____ theoretical
distribution.

(e) _____ is the difference between the parameter
and its estimate obtained from the random
sample.

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

(a) In sampling distribution, a finite population of
8 units, samples of size 4 can be selected in
50 ways.

(b) In a binomial distribution, mean > variance.

(c) Trend can be measured by moving average
method.

( 6 )

(d) Paasche’s price index is the geometric mean
of Laspeyre’s and Fisher’s price indices.

(e) In time-series analysis, the free-hand method
can represent both linear and nonlinear trends.

SECTION—II
( Marks : 30 )

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

(a) A pair of dice is thrown 200 times. If getting
a sum of 9 is considered a success, find the
mean and variance of the number of successes.

(b) Find the variance of the random variable X ,
where the probability distribution is given by
the table :

X : 0 1 2 3

P (X ) : 0·15 0·40 0·25 0·20

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

(d) State some of the important factors responsible
for non-sampling errors in any survey (census
or sample).

( 7 )

(e) What are the limitations of index number?

(f) Find the mean of the Poisson distribution.

(g) If X denotes the number of heads appear when
two coins are tossed, then by using the laws of
expectations, evaluate E (2X - 1)2 .

(h) Distinguish between seasonal variation and
cyclical variation.

(i) Define cost of living index number. State its
uses.

(j) Describe the models of a time series.

( 8 )

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

Answer four questions, taking at least one from each Group

GROUP—A

5. (a) Define the following : 1½×3=4½

(i) Mathematical expectation

(ii) Discrete random variable

(iii) Continuous random variable

(b) Show that E (a X ) = aE (X ). 3

(c) If the sum of the mean and variance of
a binomial distribution for 5 trials is 1·8,
then find the distribution. 5

6. (a) Define Poisson distribution and binomial
distribution. Mention three conditions under
which binomial distribution tends to Poisson
distribution. 1½+1½+3=6

(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] 2½

( 9 )

(c) If three persons on an average come to ABC
company for job interview, then find the
probability that less than three people have
come for interview on a given day. [Given,
e -3 = 0 × 0497] 4

GROUP—B

7. (a) What are index numbers? Explain their uses.
2+3=5

(b) Write a short note on the method of selection
of base period in the construction of an index
number. 2½

(c) From the following table, construct the
formulas of—

(i) Laspeyre’s index;

(ii) Paasche’s index. 2½×2=5

Item 2012 2017

Price Quantity Price Quantity
p 0i q 0i p1i q1i

A 4 20 6 10

B 3 15 5 20

C 2 25 3 15

D 5 10 4 40

( 10 )

8. (a) What are different types of index number? 2

(b) From the data given below, construct the cost
of living index number : 4

Group Index number Weights

Food 250 45

Rent 150 15

Clothing 320 20

Fuel and lighting 190 5

Miscellaneous 300 15

(c) Explain various methods of measuring
trend and point out their relative merits and
demerits. 6½

GROUP—C

9. (a) Enumerate and explain various stages of
a sample survey. 6½

(b) Show that

s2 N - n
V (x ) SRSWOR = ×
n N
where x and s have usual meanings. 6

( 11 )

10. (a) Suppose 4 units of a population are X 1 = 2,
X 2 = 4, X 3 = 6 and X 4 = 8. Draw all possible
samples of size 2 without replacement and
calculate their mean. Show that E (X ) = m.
Also find the variance of the estimate of the
population mean in case of—

(i) SRSWR of size 2;

(ii) SRSWOR of size 2. 2+3½+3=8½

(b) Write a note on stratified random sampling. 4

HHH

8K—50/46 HS/XII/A. Sc/S/18