B.Com. (Part III) (Semester (Old CGPA) 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
A group of some or all of given number, selecting number of things without
considering their order is called a
Permutation Combination
Both a and b None of these
nPr
None of these
5C2
10 20 16 None of these
Number of terms in the expansion of y)n is
n 1 n n 1 None of these
All possible outcomes of a random experiment forms the
Event Sample space
Both a and b None of these
When the events are mutually exclusive then p(A 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 3 then E(2X is
6 20 12 None of these
10) If k is a constant then variance of k is
k2 k 0 None of these
11) Which of the following is probability distribution
0.4, 0.5) 0.6)
0.2, 0.8) 0.4)
12) Find the constant if the probability mass function of x is
X 0 1 2
K 2K 2K
0 1/4 1/5 1
13) Probability of getting a red card, when a card is drawn from a pack of cards.
1/4 4/32 13/52 26/52
14) If A is an even and A is its complementary event then
P 1 1 P
1 P None of these
2. State and prove the relation between permutation and combination. 7
A random variable X has the following probability function as 7
X 1 2 3 4 5 6 7
K 2K 3K K2 K2 K 2K2 4K2
Find K ii) P(X iii) P x 4).
Set P
3. State and prove additive law of probability. 7
Expand x
4. Attempt any one of the following.
Define probability mass function of discrete random variate X. 14
Suppose three unbiased coins are tossed simultaneously and number of
heads is noted. Find its probability distribution and mean.
The joint pmf of Y). 14
x
y 0 1 2 3
0 c 2c 3c 4c
1 2c 4c 6c 8c
2 3c 6c 9c 12c
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 if r.v. are
independent then 14
The pmf of X is
X 0 1 2 3
1/6 1/3 1/3 1/6
Find mean and variance of X.
*SLRCO73* SLR-CO 73
Set P
Let be bivariate discrete r.v. Define 14
Marginal pmf of X
ii) Marginal pmf of Y.
The joint probability of X and Y is
x
y 1 2
1 0 1/3
2 1/3 0
3 0 1/3
Find
Marginal distributions of X and Y
ii) Are X and Y are independent
iii) Find E
iv) Find E(XY).