Question: 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 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.

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