B.Com. (Part III) (Semester (CBCS) Examination, 2018
ADVANCED STATISTICS (Paper
Day and Date Friday, 7-12-2018 Max. Marks 70
Time 10.30 a.m. to 1.00 p.m.
N.B. All questions are compulsory.
Each question carries equal marks.
Figures to the right indicate full marks.
Use of calculators is allowed.
1. Choose the most appropriate alternative amongst the given for each question. 14
From a group of given number, selecting some number of things without
considering their order is called a
Permutation Combination Both a and b None of these
nPr
8C2
10 28 16 none of these
Number of terms in the expansion of y)5 is
4 5 6 none of these
All possible outcomes of a random experiment forms the
Event Sample space
Both a and b None of these
When the event A is an impossible event then is
1 0.5 0 none of these
The probability of any event is always less than
0 1 ∞ none of these
If A and B are independent then
p(A
All of the above
If E 8 then E(2X is
16 22 12 none of these
10) The parameters in Poisson distribution are
One Two Three None of these
11) Which of the following is not a probability distribution
0.4, 0.4) 0.6)
0.8) 0.4)
12) Find the constant if the probability mass function of x is
X 0 1 2
K 2K 5K
0 1/4 1/8 1
13) Probability of getting a king card, when a card is drawn from a pack of
cards.
1/2 4/32 13/52 4/52
14) If A is an event and A is its complementary event then
− 1
1− none of these
2. State and prove the relation between Permutation and Combination. 7
A random variable X has the following probability functions as 7
X 1 2 3 4 5 6 7
0 2K 3K K2 K2 2K2 2K2
Find K ii) P(X iii) P(1 X
3. State and prove additive law of probability. 7
Define Poisson distribution. State its mean and variance. Give two real life
situations where poisson distribution is useful. 7
4. Attempt any one of the following.
Define probability mass function of discrete random variate X. 14
Suppose two dice are thrown and sum of numbers on the upper faces of
the two dice are noted. Find its probability distribution.
Set P
The joint pmf of Y). 14
0 1 2 3
0 0 c 4c 9c
1 c 2c 5c 10c
Find
c
ii) P(X Y
iii) Conditional distribution of X given Y 2
iv) Conditional distribution of Y given X 0.
5. Attempt any one.
Define mathematical expectation of r.v.X. Prove that
E(X E E 14
The pmf of X is
X 0 1 2 3
0.3 0.4 0.2 0.1
Find mean and variance of X. 14
Let be bivariate discrete r.v. Define
Marginal pmf of X
ii) marginal pmf of Y
The joint probability of x and Y is
1 2
1 0 1/3
2 1/3 0
3 0 1/3
Find
Marginal distribution of X and Y
ii) Are X and Y are independent
iii) Find E
iv) Find E