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

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Given an event A, define the conditional expectation of Y given A as E[YI] P(A) E[Y|A] =

where IA 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,

if C< 250 х C - 250 if C > 250.

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

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
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