Hey everyone, I recently started studying for the P exam and I've just started expected values. There's a question in the study guide about finding expected values of minimums that I don't really understand.

Q: The pdf of a loss is f(x)=0.5e^(-0.5x), x>0. An insurance will pay the entire loss up to a maximum of 1. Calculate the expected value of the payment.

The first step is:

E(X^1)=integral of [1-F(X)]dx from 0 to 1

Could someone please explain where this step came from? I'd appreciate it a lot.

Q: The pdf of a loss is f(x)=0.5e^(-0.5x), x>0. An insurance will pay the entire loss up to a maximum of 1. Calculate the expected value of the payment.

The first step is:

E(X^1)=integral of [1-F(X)]dx from 0 to 1

Could someone please explain where this step came from? I'd appreciate it a lot.

## Comment