I know A1 and A2 to be Poisson distributed with (unknown) means x1 and x2.

I have a single measurement of both: n1 and n2. I want to test the zero hypothesis that x1=x2.

Example: number of problems in an appliance over one year follows a Poisson dist. I have two appliances. One had 10 problems over the year, and the other had none. Can I conclude there is a real difference in the underlying mean numbers of problems per year? what is the p-value?

I look for a statistic that would have a lambda independent distribution, and a value that would be "small" for identical dist. My first guess was (n1-n2)^2/(n1+n2) which has the right scaling but does not work (besides having a problem at n1=n2=0).

Ideas anyone?