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

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23. 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

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: 9780123756862

10th Edition

Authors: Sheldon M Ross

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Question Posted: Sep 16, 2024 03:01 AM

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

Question:

n P(X = n) = (" = 1) p' (1 - p)*-*, nr

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Introduction To Probability Models

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n P(X = n) = (" = 1) p' (1 - p)-, nr