6 students were asked how many times they rebooted their computers

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6 students were asked how many times they rebooted their computers

Problem 6

6 students were asked 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?

Hint
Statistics"Probability mass functions :A probability mass function is a function which gives the probability that a discrete random variable is basically equal exactly to some of the value. Most of the times it is also called as the discrete density function. Also, the probability mass function is a probability measure which, for a random variable, gives the probabilities of the possible values."...

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