Let X be a random variable. Say whether the following statements are true or false, and explain what is wrong with any false statements.

a. Mean, expectation, and average are all terms used to describe E(X).

b. The mean is a fixed constant, but the variance varies.

c. E(X) and Var(X) are random variables.

d. Var(X) is a measure of the spread of the distribution of X.

e. If you draw n random numbers from the distribution of X, add them up and divide by n, your answer will approach E(X) as n gets large.

f. If you draw n random numbers from the distribution of X, add up their squares and divide by n, your answer will approach Var(X) as n gets large.