(a) Let X be uniform on the interval [0,2], and define Y = 2X +1. Find the PDF, CDF, expectation, and variance of Y.

(b) Let X and Y have joint distribution f(x, y) = ( cxy+1/4 x [1,2] and y [0,2] 0 else Find the constant c. Are X and Y independent?

(c) Let X Exp(3). What is the probability that X [0,1]? If I define a new random variable Y = bXc, for each k N, what is the probability that Y = k? Do you recognize this (discrete) distribution?

(d) Let Xi Exp(i)for i = 1,...,n be mutually independent. It is a (very nice) fact that min(X1,...,Xn) Exp(). Find .