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Question 1. We asked 6 students how many times they rebooted

Question 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).

Create a joint probability table for C and R. Be sure to include the marginal probability mass functions.

Compute E(C) and E(R).

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.

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

Calculate P (W > M).

What is the correlation between W and M?

Question 2.

Recall the relation between degrees Fahrenheit and degrees Celsius

                                                               Degree Celsius = 5/9. degrees Fahrenheit ? 160/9

Let X and Y be the daily high temperature in degrees Fahrenheit for the summer in Los Angeles and San Diego. Let T and S be the same temperatures in degrees Celsius.

Suppose that Cov(X, Y ) = 4 and ?(X, Y ) = 0.8 . Compute Cov(T, S) and ?(T, S) (?(T, S) = correlation)


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