I have the following problem set at hand:
The random variable $\xi$ has Poisson distribution with the parameter $\lambda$. If $\xi=k$ we perform $k$ Bernoulli trials with the probability of success $p$. Let us define the random variable $\eta$ as the number of successful outcomes of Bernoulli trials. Prove that $\eta$ has Poisson distribution with the parameter $p\lambda$.
I feel confused about what to do exactly with the $\xi=k$ part of the question? I was trying to do a $\lambda = np$ substituion and let n go to infinity, but i cannot reach at the desired prove. Could someone help to guide me through this?