Thread: Poisson Sampling

Hi, here's the question:
Let be independent r.v.s with the Poisson distribution of parameter .
Let . Find the support and probability mass function of the distribution of . Calculate and .
Any help would be appreciated. Thanks.

I get using linearity. Also, . But this is no longer a Poisson since the mean and variance are different?? If that's true then . Is this right?

Originally Posted by davidmccormick

I get using linearity. Also, . But this is no longer a Poisson since the mean and variance are different?? If that's true then . Is this right?

Indeed is no longer a Poisson r.v., but you could have seen that directly from the question about the support of . While are integers, their mean may not be an integer. The support of the distribution of is "the set of possible values" for Y (You can remove the " " in the present situation). Therefore, it is...

And in order to determine the probability mass function of Y, you should first find that (or recall that) of . It is Poisson with parameter . Then giving the probability mass function of Y should be simple. Tell us if you still have problems.

(and yes of course )

Just let and find it's distribution.

Then insert the n, since