Consider the sum Sn=∑i=1nXiS_n = \sum_{i=1}^n X_iSn=∑i=1nXi where Xi∼Poisson(λi)X_i \sim \text{Poisson}(\lambda_i)Xi∼Poisson(λi). What is the distribution of SnS_nSn?
Normal(∑λi,∑λi\sum \lambda_i, \sum \lambda_i∑λi,∑λi)
Poisson(∏λi\prod \lambda_i∏λi)
Gamma(∑λi,1\sum \lambda_i, 1∑λi,1)
Poisson(∑λi\sum \lambda_i∑λi)