if X is a Poission distributed random variable with a mean o

if X is a Poission distributed random variable with a mean of 3 and Y is another Possion distributed random vaariable with a mean of 2 and the two are independant . what is the variance of the sum X + Y?

Solution

if X and Y are independent poisson, then (X+Y) is also poisson with mean (rate) = 3+2 = 5

For poisson, variance = mean = 5