Given an event A, define the conditional expectation of Y given A as
![](https://test.transtutors.com/qimg/20195c7a-4e9c-4886-8c96-736b3909177b.png)
where IA is the indicator random variable.
(a) Let Y ∼ 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,
![](https://test.transtutors.com/qimg/5eec18a0-575f-45c6-976f-850bccac93dd.png)
Find E[X], the expected payout by the insurance company.