Q 4.3. A fair die is rolled until a 6 is obtained. Let Y be the total number of rolls and X the number of 1s. 1. Compute the distribution of Y. 2. For a fixed k ≥ 1, find the distribution of X given Y = k. 3. Compute E(X) and Var(X).

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Q 4.3. A fair die is rolled until a 6 is obtained. Let Y be the total number of rolls and X the
number of 1s.
1. Compute the distribution of Y.
2. For a fixed k ≥ 1, find the distribution of X given Y = k.
3. Compute E(X) and Var(X).
Transcribed Image Text:Q 4.3. A fair die is rolled until a 6 is obtained. Let Y be the total number of rolls and X the number of 1s. 1. Compute the distribution of Y. 2. For a fixed k ≥ 1, find the distribution of X given Y = k. 3. Compute E(X) and Var(X).
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