1. Let x be a Poisson rv, with alphabet
a) Find the value of for which P [x = 2] is maximized.
b) Show that the probability P [x > 2] as a function of is continuous and monotonically increasing.
c) Calculate E [ex].
2. Let x a Gaussian rv
a) Find the PDF of y = x2 + 1.
b) Calculate E x2(x + 1 + sin x).
