# Thread: Mean and variance with parameter

1. ## Mean and variance with parameter

I am having trouble with this particular problem and could use some help.

Let N be accidents that occur in a year and it is a Poisson distribution with parameter t.
S = X1 + X2 + ... + Xn where Xi is the amount of the insurance claim for the accident. Xi are iid with a mean "u" and variance "o^2"

How do you find the mean and variance of S?
Mean is n * u and variance n * (o^2)
But N is poisson so this varies?

2. Originally Posted by cubs3205
I am having trouble with this particular problem and could use some help.

Let N be accidents that occur in a year and it is a Poisson distribution with parameter t.
S = X1 + X2 + ... + Xn where Xi is the amount of the insurance claim for the accident. Xi are iid with a mean "u" and variance "o^2"

How do you find the mean and variance of S?
Mean is n * u and variance n * (o^2)
But N is poisson so this varies?
Try using Wald's equation: Wald's equation - Wikipedia, the free encyclopedia