Folks:
I have a seemingly simple question, but cannot resolve it (at least without much of thinking and digging.
Suppose that "n" is a Poisson random variable drawn from the distribution with Poisson lambda "lambda". What is the distribution of the random variable A*n, where A is an arbitrary real number?
Please, note, I am not asking how to generate this random variable, I still remember how to multiply a set of numbers by a constant. I am asking about analytical form of this distribution, and about how to derive the distribution function (or density) in their analytical form.
A standard approach through the characteristic functions did not bring immediate success. I am sure there there are a lot of smart people in the list who would consider this problem very simple. Please, help.
Thanks in advance.
Jewel |