Problem 1. We asked 6 students how many times they rebooted their computers last week. There were 4 Mac users and 2 PC users. The PC users rebooted 2 and 3 times. The Mac users rebooted 1, 2, 2 and 8 times. Let C be a Bernoulli random variable representing the type of computer of a randomly chosen student (Mac = 0, PC = 1). Let R be the number of times a randomly chosen student rebooted (so R takes values 1,2,3,8). (a) Create a joint probability table for C and R. Be sure to include the marginal probability mass functions.

(b) Compute E(C) and E(R).

(c) Determine the covariance of C and R and explain its significance for how C and R are related. (A one sentence explanation is all that’s called for.

Are R and C independent?

(d) Independently choose a random Mac user and a random PC user. Let M be the number of reboots for the Mac user and W the number of reboots for the PC user.

(i) Create a table of the joint probability distribution of M and W , including the marginal probability mass functions.

(ii) Calculate P (W >M).

(iii) What is the correlation between W and M?​