Q1. (25 points) The amount of time (in hours) that Chao spends checking email each day is a random variable X. A day is a heavy email day" if Joe spends at least 45 minutes on checking email that day. Assume that the density function of X is given by f(x) { x2 if 0x1 C if 2x < 3 otherwise 0 (a) (5 points) What is the probability that Chao spends more than 15 minutes checking email on Thursday? (b) (5 points) On average, how many minutes does Chao spend each day checking email? (c) (5 points) Compute P(0.75 < X 2.2|X > 0.5). (d) (5 points) Compute P(X = 2), P(X = 0), P(X = E[X]), P(X > E[X]), and F(E[X]). (f) (5 points) What is the probability that there are an odd number of heavy email days in October?