# The sum of n independent poisson($\lambda_i$) random variables is poisson($\sum_1^n \lambda_i$) random variable. [duplicate]

How can I show that the sum of n independet poisson random variables is a poisson random variable? I need to conclude that the sum of i.r.v with distribution $Poisson(\lambda_i)$, i=1,...,n, is $Poisson(\sum_1^n \lambda_i)$.