I'm trying to play around with two random variables and I can't get wolfram alpha to parse my input.

I've tried something really simple that like `

PDF(X+Y) where X and Y are iid Poisson(lambda)` trying to get wolfram alpha to tell me that this is Poisson(2*lambda) or even just give me the joint cdf or pdf.

all I can get out is `

Using closest Wolfram|Alpha interpretation: Poisson(lambda)` I really want the distribution of `

X/(X+Y) where X and Y are iid Poisson(lambda)` but I figured I would start small.

any ideas what I could try to help it interpret my input?