Answer true or false. Explain your answer.
Let X and Y be random variables.
(a) The expectation of a random variable is the outcome that is most likely to occur.
(b) If X and Y are independent, then var(X + Y ) = var(X) + var(Y ).
(c) If X and Y are independent, then the value of the conditional expectation E(Y |x)
is not affected by changes in x.
(d) Zero correlation, corr(X,Y ) = 0, implies that X and Y are independent.