Suppose X and Y are independent random variables with X following a uniform distribution on (0,1) and Y exponentially distributed with parameter Lambda = 1.
a) Find the density for Z = X + Y. Verify that it integrates to 1. Find the median (the value of z for which P(Z =< z) = 1/2)
b) find E(X - Y) and var(X - Y). Find E(ZX)