Question: Please provide detail solution 3. (15 points) You roll a dice until you get a six. Denote the number of rolls you need by X.

Please provide detail solution

3. (15 points) You roll a dice until you get a six. Denote the number of rolls you need by X. Then, you flip a fair coin repeatedly until you get X heads. Denote the number of coin flips you need by Y. (a) (4 points) Find E[Y]. Please do this before computing the probabilities in parts b and C. (b) (4 points) Find P(Y = n|X = k) (c) (7 points) Compute P(Y = n). Identify the distribution of Y. Hint: The binomial theorem might be useful here: (a + b)" = ER- ()akbn-k./

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