BSc Sem I 2023 2024 Dec 2024 STATISTICS II Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q2 of calculator is allowed
   • (a) State true and false, with justification. [Each 2 marks]
2. Q1 random space must contain a finite number of elements
3. Q2 If A’ and B are independent, then A and B are independent
4. Q5 Poisson distribution is always negatively skewed
   • (b) Answer in one line. [Each 2 marks]
5. Q1 Give an example of (i) mutually exclusive (ii) exhaustive event
6. Q2 State multiplicative theorem for three events
7. Q3 Define probability mass function of random variable X
8. Q4 Define covariance between two random variable
9. Q5 Define bernoulli experiment Attempt any TWO. [Each 10 marks]
   • (1) State and prove Bayes’ theorem
   • (2) (a)Explain the concept of conditional probability ‘ (b) Define pair-wise independence and total independence
   • (3) (a) Suppose a card is drawn from a well shuffled pack of cards. Let event A: getting heart card and B: getting queen. Are A and B independent?
   • (b) A husband and a wife appear for two vacancies in the same post. The probability of husbands selection is 1/6 and wife’s selection is 1/5 , what is the probability that
   • (i) both will be selected (ii) only one of then would be selected (iii) none of them would be selected?
10. Q3 Attempt any TWO, [Each 10 marks]
    • (1) Define Cumulative distribution and its Properties. And prove E(aX+b) =
    • (2) Define covariance between two random varibles. State and prove its properties
    • (3) If bivariate probability mass function is given by Obtain the value of K. Also obtain marginal p.m.f. of X and Y. and conditional
    • p.m.f. of X given Y = 2
11. Q4 Attempt any TWO. [Each 10 marks]
    • (1) (a) If a random variable X follows binomial distribution with parameters (n,p), Obtain expression for its mean & variance VCD/ FYBSC-SEM I STATISTICS II 100 MARKS - 3 HRS
    • (b) If a random variable X follows Poisson distribution with parameters x Obtain expression for its mean & variance
    • (2) (a) If a discrete random variable X has uniform distribution over the range : And its mean is 12.5 find n and its variance
    • (b) For binomial variate X with parameter (n,p); p=q and P(X=2) = P(X=3),Find @
    • (3) (a) If random yariable X follows Poisson distribution , if P(X=5) = 0.3 P(X=4) then find mean and P(X > 3)
    • (b) A small voting district has 101 female voters and 95 male voters. A random sample of 10 voters is drawn.What is the probability that exactly 7 of the voter will be female? (using hypergeometric distribution)
12. Q5 Attempt any TWO. [Each 10 marks]
    • (1) State and prove the addition theorem of probability concerning 2 events A and B
    • (2) (a)If bivariate p.m.f is given by Obtain the value of k. also obtain marginal probabilities of X and Y. Are X and Y
    • (b) Consider the experiment of tossing four unbiased coins. The random variable X is number of heads observed and Y be the number of heads observed in asequence Then write down joint probability mass function of X,Y. Hence their maginal probability, also obtain conditional p.m.f. of X given Y = 2
    • (3) (a) An unbiased dice is rolled. Write down the p.m.f for the number on the uppermost face. Obtain its mean and variance
    • (b) A box contain 10 balls of which 6 are red and 4 are white. Two balls are selected at random. If X denotes number of white balls selected then write down p.m.f. of and also state mean and variance of X

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