Then we can deduce the mean and variance of from the mean and variance given and the law of :
(thanks to computations with the binomial and Poisson distribution), hence
OR: In fact, you can prove (or perhaps you already know) that is a Poisson random variable of parameter , so that the above is immediate. A possible proof uses generating functions... Otherwise, if you know Poisson processes, this is a standard property: if we extract points independently with probability , we get another Poisson process with intensity .