Let N,X1, X2... be random variables where N has a poisson distribution with mean 3 while X1, X2...each has a Poisson distribution with mean 7.
a) Determine
b) Determine the variance of
I have no idea where to start. Please give me a hand. Thanks
Let N,X1, X2... be random variables where N has a poisson distribution with mean 3 while X1, X2...each has a Poisson distribution with mean 7.
a) Determine
b) Determine the variance of
I have no idea where to start. Please give me a hand. Thanks
Hello,
If you know no formula for this, the best way is to partition the set of events :
(assuming that N and the sequence X_i are independent, and I guess there's an extra N in what you wrote... anyway, it would be the same reasoning)
And
The sum of Poisson variables is a Poisson variable (whose parameter is the sum of the parameters)
And you have to see what happens if N is 0. This should be stated in your problem, or conventionally, the sum would be 0.
It's a bit messy, but you can get the information you need from here...
It looks like you have an extra N in the expectation.
This is Wald's equation, see...
Wald's equation - Wikipedia, the free encyclopedia