With reference to Exercise 16, find expressions for μY and ![](https://test.transtutors.com/qimg/3a1e9908-0450-4167-8057-82e4f4cee67d.png)
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
![](https://test.transtutors.com/qimg/fc865c40-3d99-43fb-b787-3d9b40b3494d.png)