### Parameter-Mix Distributions

The notation:

denotes a distribution in which parameter (instead of being fixed) has an distribution. We wish to find the unconditional distribution of ...

Given: The pmf of is :

Given: The pdf of parameter is :

Then, the parameter-mix distribution is the expectation with respect to the distribution of Θ. The solution with **mathStatica** is simply:

with domain of support:

This is known as Holla's distribution. Here is a plot of its pmf when and :

**Fig. 1: ** The pmf of Holla's distribution when and