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8 Roll a fair (standard) die until a 6 is obtained and let Y be the...

8 Roll a fair (standard) die until a 6 is obtained and let Y be the total number of rolls until a 6 is obtained. Also, let X the number of 1s obtained before a 6 is rolled.

(a) Find E(Y).

(b) Argue that E(X | Y = y) = 1/5 (y − 1). [Hint: The word “Binomial” should be in your answer.]

(c) Find E(X).

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