More specifically, if X and Y are Poisson-distributed, what is the variance of X/Y (assuming that X and Y are independent)?

Thanks!

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- Mar 22nd 2010, 05:43 PMfloatsWhat is the variance of the division of 2 random variables?
More specifically, if X and Y are Poisson-distributed, what is the variance of X/Y (assuming that X and Y are independent)?

Thanks! - Mar 23rd 2010, 01:01 AMLaurent
- Mar 23rd 2010, 06:35 AMfloats
I see, that is a good point.

What if we consider X/(Y+1) instead? What would the variance of that be? - Mar 23rd 2010, 11:20 AMLaurent
To get the variance, you need the expectation, and the expectation of the square. Since the variables are independent, you need and . I guess you know how to get and ( and since I know the variance is ). So let's consider the other ones.

; then let in the sum to see that it equals .

is more tricky. I'd let and compute , which we have computed above ; now integrate to get , and multiply by to get . - Mar 23rd 2010, 12:23 PMfloats
I got the part but was struggling with the part.

Thanks for the help!