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You roll a fair 6 sided die 5 times. Let Xi be the number of times...

You roll a fair 6 sided die 5 times. Let Xi be the number of times an i was rolled for i = 1, 2, . . . , 6.

(a) What is E[X1]?

(b) What is Cov(X1, X2)?

(c) Given that X1 = 2, what is the probability the first roll is a 1?

(d) Given that X1 = 2, what is the conditional probability mass function of, pX2|X1 (x2|2), of X2?

(e) What is E[X2|X1]

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