i need mathematical proof of Probability mass function of negative binomial distribution.

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- May 29th 2011, 11:53 PMmuhammadResearch
**i need mathematical proof of Probability mass function of negative binomial distribution.**

- May 30th 2011, 02:43 AMSpringFan25
all trials are independent. The chance of the kth failure happening on the nth trial is:

P(k-1 failures in n-1 trials) x P(nth trial is a failure)

The first term is just the "regular" binomial pmf (with suitable parameters) and the second term is (1-p). - May 30th 2011, 03:41 AMmuhammadResearch problem
Thanks for reply to post, can we do it use induction (as binomial ) by expressing negative binomial as sum of geometric random variable

- May 30th 2011, 04:49 AMmr fantastic
You need to do the research. Go to your institute's library. Find this book: Amazon.com: Univariate Discrete Distributions (Wiley Series in Probability and Statistics) (9780471272465): Norman L. Johnson, Adrienne W. Kemp, Samuel Kotz: Books

Read it.