Question

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

Answer 1

answers are all correct