Explain whether the following statements are true or false. Give reasons.
a. Although the expected value of an r.v. can be positive or negative, its variance is always positive.
b. The coefficient of correlation will have the same sign as that of the covariance between the two variables.
c. The conditional and unconditional expectations of an r.v. mean the same thing.
d. If two variables are independent, their correlation coefficient will always be zero.
e. If the correlation coefficient between two variables is zero, it means that the two variables are independent.
f. E(1 / X) = 1 / E(X)
g. E[X - µX]2 = [E(X - µX)]2