For the population of Cal Poly students, let X = number of hours slept in the...

For the population of Cal Poly students, let X = number of hours slept in the last 24 hours and Y = number of exams today. Consider the following (admittedly simplistic) joint probability distribution for Xand Y.

			x
		5	6	7	8
	0	.01	.09	.16	.18
y	1	.11	.06	.04	.02
	2	.28	.02	.02	.01

For your convenience, I have calculated the following: ?(?)=6.24,?(?2)=40.34,?(?)=0.89,?(?2)=1.55E(X)=6.24,E(X2)=40.34,E(Y)=0.89,E(Y2)=1.55.

A. Determine the marginal distribution of X.

B. Calculate E(XY).

C. Calculate the correlation between X and Y. Don’t round at intermediate steps. Give your final answer to three decimal places.

D. Interpret the correlation value in the context of this example.

E. Are X and Y independent random variables? How can you tell?

Expert Solution

orchestra answered 2 years ago

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