For a sequence of independent Bernoulli trials, Y is the number of successes before the kth failure.

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For a sequence of independent Bernoulli trials, Y is the number of successes before the kth failure. Explain why its probability mass function is the negative binomial,

(y + k – 1)! y!(k – 1)! P(y) - π'(1 - π)*, y = 0,1,2, ... .

[For it, E(Y) = kÏ€/(1€“Ï€) and var(Y) = kÏ€/1(1€“Ï€)², so var(Y) > E(Y); the poisson is the limit as k †’ ˆž and Ï€ †’ 0 with kÏ€ = µ fixed.]

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Categorical Data Analysis

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Authors: Alan Agresti

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Question Posted: Oct 10, 2018 01:31 PM

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For a sequence of independent Bernoulli trials, Y is the number of successes before the kth failure.

Question:

(y + k – 1)! y!(k – 1)! P(y) - π'(1 - π)*, y = 0,1,2, ... .

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Categorical Data Analysis

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