Thread: find the distribution of the sum of 25 ind poisson rv's

Find the distribution of the sum of 25 independent Poisson random variables with the identical parameter λ = 5

Hello,

Originally Posted by plm2e

This is confusing me and i would appreciate any help i can get.

Find the distribution of the sum of 25 independent Poisson random variables with the identical parameter λ = 5

Use moment generating function, by remembering that the mgf of the sum of independent rv equals the product of their mgf.

(you should find the mgf of a Poisson distribution with parameter 25x5)

ok so, Mx(t) = e^[λ((e^t)- 1))]

i get e^[5((e^25) - 1)] = my ti 83 says overflow

i think i may be confused on what t is

missed the product part on my last post, but im still concerned about what the t means in the mgf

Originally Posted by plm2e

ok so, Mx(t) = e^[λ((e^t)- 1))]

i get e^[5((e^25) - 1)] = my ti 83 says overflow

i think i may be confused on what t is

Let be iid Poisson rv with parameter 5.

Then their mgf is :

The mgf of is :



And this is the mgf of a Poisson distribution with parameter 125.