Problem 3. (25 points) The amount of time (in hours) that Marc spends checking email each day is a random variable X. A day is a “heavy email day” if Marc spends at least 45 minutes on checking email that day. Assume that the density function of X is given by f(x) = x 2 , if 0 ≤ x < 1; C, if 2 < x < 3; 0, otherwise. (a) (5 points) What is the probability that Marc spends more than 15 minutes checking email on Thursday? (b) (5 points) On average, how many minutes does Marc 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)). (e) (5 points) What is the probability that there are an odd number of heavy email days in October?