For each of the following statements, state whether it is true (meaning, always true) or false (meaning, not always true):
1. 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.
2. Suppose that, E[X]=0 . Then, X=0 .
3. Suppose that, E[X2]=0 . Then, P(X=0)=1 .
4. Let X be a random variable. Then, E[X2]≥E[X] .
5. Suppose that, X is a random variable, taking positive integer values, which satisfies E[(X−6)2]=0 . Then, pX(4)=pX(5) .
6. Suppose that E[X]≥0 . Then, X≥0 with probability 1, i.e., P(X≥0)=1 .
Answers:
1.
a) False
b) False
c) True
2. False
3. True
4. False
5. True
6. False
1 answer
2 answers