Suppose we roll a six sided die repeatedly. Let Ni be the number of the roll on which we see i for the first time.   (a) Find the marginal distributions of N1.   (b) The conditional distribution of N6 given N1 = i   (c) Find the joint distribution of N1 and N6.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Suppose we roll a six sided die repeatedly. Let Ni be the number of the roll on which we see i for the first time.

 

(a) Find the marginal distributions of N1.

 

(b) The conditional distribution of N6 given N1 = i

 

(c) Find the joint distribution of N1 and N6.

Please answer all subparts with explanation.

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