(13 total points) The pdf of a random variable X is given by () = ( + + 2) 0 for 0 1 otherwise

a. (4 pts) Show that this expression is a true pdf (meaning that it satisfies the two properties mentioned in class)

b. (3 pts) Calculate E(X).

c. (4 pts) The random variable Y has a Poisson(4) distribution. Calculate the probability that Y is more than one standard deviation below its mean.

d. (2 pts) If X and Y are independent, what is E(XY)?