# Thread: Expected value of a function depending on a r.v.

1. ## Expected value of a function depending on a r.v.

If the number of accidents per day, Y, is assumed to have a Poisson distribution with mean 10, how can I find the expected cost to an insurance company per day, X, where X = 2000 - 3Y - Y^2?

Thanks,

Paul

$E(X) = E(2000) - 3 E(Y) - E(Y^2) = 2000 - 3 (10) - E(Y^2)$.
So the speed bump is getting $E(Y^2)$. There are several ways of getting it. Here's the simplest:
Recall that $Var(Y) = E(Y^2) - [E(Y)]^2$. You know Var(Y) and E(Y) so you can substitute and solve for $E(Y^2)$.