1. Let x be a Poisson rv, with alphabet a) Find the value of for which P [x = 2] is maximized. b)…

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).