Suppose that the number of events occuring in a given time period is a Poisson random variable with parameter λ. If each event is classified as a type i event with probability $\displaystyle p_i$, i = 1,...,n, sum of $\displaystyle p_i$ = 1, independently of other events, show that the numbers of type i events that occur, i = 1,...,n, are independant Poisson random variables with parameters λ$\displaystyle p_i$, i = 1,...,n.

I am finding this very unclear and confusing. or maybe I'm jsut burnt out from the rest of my studying

Anyone have any advice/ideas that could help clear this up.