The negative binomial distribution is sometimes defined in a different way as the distribution of the number

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 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.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...