(Created page with "'''2. (25 Points)''' Let <math class="inline">\mathbf{X}</math> and <math class="inline">\mathbf{Y}</math> be independent Poisson random variables with mean <math class="in...") |
(No difference)
|
Revision as of 01:28, 9 March 2015
2. (25 Points)
Let $ \mathbf{X} $ and $ \mathbf{Y} $ be independent Poisson random variables with mean $ \lambda $ and $ \mu $ , respectively. Let $ \mathbf{Z} $ be a new random variable defined as $ \mathbf{Z}=\mathbf{X}+\mathbf{Y}. $
(a) Find the probability mass function (pmf) of $ \mathbf{Z} $ .
(b)Find the conditional probability mass function (pmf) of $ \mathbf{X} $ conditional on the event $ \left\{ \mathbf{Z}=n\right\} $ . Identify the type of pmf that this is, and fully specify its parameters.
Note
This problem is identical to the example: Addition of two independent Poisson random variables.
