A coin having probability p of coming up heads is successively flipped until the rth head appears.

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A coin having probability p of coming up heads is successively flipped until the rth head appears. Argue that X, the number of flips required, will be n, n ≥ r, with probability P{X = n} =

n −1 r −1

pr (1 −p)n−r, n≥ r This is known as the negative binomial distribution.

Hint: How many successes must there be in the first n−1 trials?

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Introduction To Probability Models

ISBN: 9780443187612

13th Edition

Authors: Sheldon M. Ross

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Question Posted: Sep 19, 2024 10:06 PM

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A coin having probability p of coming up heads is successively flipped until the rth head appears.

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Introduction To Probability Models

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