Thread: 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

Originally Posted by Canadian0469

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

.

So the speed bump is getting . There are several ways of getting it. Here's the simplest:

Recall that . You know Var(Y) and E(Y) so you can substitute and solve for .