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Unformatted text preview: X x i E ( Y  X = x i ) p X ( x i ) if X is discrete with pmf p X ; EY = E ( E ( Y  X )) = Z ∞∞ E ( Y  X = x ) f X ( x ) dx, if X is continuous with pdf f X . Example : The number of claims arriving to an insurance company in a week is a Poisson random variable N with mean 20. Assume that the amounts of diﬀerent claims are independent exponentially distributed random variables with mean 800. Assume that the claim amounts are independent of the number of claims arriving in a week. Find the expected total amount of claims the company receives in a week. • The formula of the double expectation EY = E ( E ( Y  X )) is a device to compute expectations by conditioning . • There is a device to compute variances by conditioning : for any two random variables X and Y Var Y = E (Var( Y  X )) + Var( E ( Y  X )) ....
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This note was uploaded on 12/03/2010 for the course OR 3500 taught by Professor Samorodnitsky during the Fall '09 term at Cornell University (Engineering School).
 Fall '09
 SAMORODNITSKY

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