P1) A discrete random variable N has the following probability mass function (PMF). 0.2, n= 0 f (n) = P(N = n) = 10.7 1 = 1 0.1 n = 2 0, otherwise. a) Find the expected value of N, E(N). [3 points] b) Find the expected value of N', E(N'). [4 points] c) Find the variance of N, var(N). [4 points] d) Find the variance of another random variable W, var(W), where W = 3-2N. [4 points] P2) Let X be a Gaussian random variable with the following probability density function (PDF) f(x)= = 1x-212 a) What are the expected value and the standard deviation of X? [4 points] For the following probabilities in parts b and c, represent the final answer in terms of P(Z 4). [3 points] c) Find P(-3