Given an event A, define the conditional expectation of Y given A as where I A is the indicator random variable. (a) Let Y ¼

Given an event A, define the conditional expectation of Y given A as 

where I_A is the indicator random variable.
(a) Let Y ˆ¼ Exp(λ). Find E[Y|Y >1].
(b) An insurance company has a $250 deductible on a claim. Suppose C is the amount of damages claimed by a customer. Let X be the amount that the insurance company will pay on the claim. Suppose C has an exponential distribution with mean 300. That is,

Find E[X], the expected payout by the insurance company.

E[YI] P(A) E[Y|A] = if C < 250 C - 250 if C > 250.