With reference to Exercise 5.16, [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 =

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With reference to Exercise 5.16,

[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 5.4. (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 b∗(x; k, θ) = (x − 1 k − 1) θ^k (1 − θ )^(x−k) for x = k, k + 1, k + 2,....)]

find expressions for μY and σ^(2/Y)

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