Q1)  Which probability distribution is suitable when events of interest happen arbitrarily, independently of one another, and rarely?

a) Binomial distribution

b) Hypergeometric distribution

c) Poisson distribution

d) Any discrete probability distribution      

Q2) Which probability distribution is suitable when sampling without replacement?

a) Hypergeometric distribution.

b) Binomial distribution.

c) Poisson distribution.

d) All of the above answers are correct.

Q3) The mean of Poisson random variable x, where λ is average number of times that event happens in certain period of time or space, is

a) λ.

b) λ ².

c) √ λ.

d) λ +1.

Q4)  If X and Y are any random variables, which of given identities is not always true?

a) E (X+Y) = E(X) + E(Y) 

b) Var(X+Y) = V(X) + V(Y)

c) E(4X+5Y) = 4E(X) + 5 E(Y) 

d) Var(4X+5Y) = 16V(X) + 25V(Y) + 40COV(X,Y)

Q5) If X and Y are arbitrary variables with E(X) = 5 and E(Y) = 8, then E(2X+3Y) is:

a) 34.

b) 13.

c) 18.

d) 40.

Q6) If X and Y are arbitrary variables with Var(X) = 7.5, Var(Y) = 6 and Cov(X,Y) = 4, then Var(2X+3Y) is:

a) 132.

b) 37.

c) 88.

d) 33.