Posted by **qwerty** on Tuesday, March 4, 2014 at 11:37am.

For each of the following statements, determine whether it is true (meaning, always true) or false (meaning, not always true). Here, we assume all random variables are discrete, and that all expectations are well-defined and finite.

Let X and Y be two binomial random variables.

a) If X and Y are independent, then X+Y is also a binomial random variable.

b) If X and Y have the same parameters, N and P , then X+Y is a binomial random variable.

c) If X and Y have the same parameter P , and are independent, then X+Y is a binomial random variable.

d) Suppose that E(X)=0 . Then, X=0 .

e) Suppose that E(X^2)=0 . Then, P(X=0)=1 .

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