The sum of n independent poisson($\lambda_i$) random variables is poisson($\sum_1^n \lambda_i$) random variable.
127394
Induction for sum of Poisson distributed random variables
3346
Proof that Conditional of Poisson distribution is Binomial
54461
Showing independence of random variables
149781
Probability of Independent Normal Random Variables
51587
Sum of Bernoulli random variables with different success probabilities
54002
Finding the distribution of the sum of three independent uniform random variables
81643
Proof that the hypergeometric distribution with large $N$ approaches the binomial distribution.
9006
Normal approximation to the Poisson distribution
45220
Proving the sum of two independent Cauchy Random Variables is Cauchy
57917
Convergence of moments of binomial to Poisson
102505
Expected number of (0,1) distributed continuous random variables required to sum upto 1
106140
The sum of two symmetric random variables is symmetric
152495
Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
126669
UMVUE of $e^{-\lambda}$ from poisson distribution
71794
Compute the mean of $(1 + X)^{-1}$ where $X$ is Poisson$(\lambda)$
58206
Poisson Distribution of sum of two random independent variables $X$, $Y$
93922
sum of noncentral Chi-square random variables