The negative binomial distribution

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With reference to Exercise 16, find expressions for μY and

Exercise 16

The negative binomial distribution is sometimes defined in a different way as the distribution of the number of failures that precede the kth success. If the kth success occurs on the xth trial, it must be preceded by x - k failures. Thus, find the distribution of Y = X - k, where X has the distribution of Definition 4.

DEFINITION 4

NEGATIVE BINOMIAL DISTRIBUTION A random variable X has a negative binomial distribution and it is referred to as a negative binomial random variable if and only if

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