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Unformatted text preview: if X is continuous with pdf f X . Var( E ( Y  X )) = X x i ( E ( Y  X = x i )) 2 p X ( x i ) X x i E ( Y  X = x i ) p X ( x i ) 2 if X is discrete with pmf p X ; Var( E ( Y  X )) = Z ∞∞ ( E ( Y  X = x )) 2 f X ( x ) dx±Z ∞∞ E ( Y  X = x ) f X ( x ) dx ² 2 if X is continuous with pdf f X . Example : Back to the example where the number of claims arriving to an insurance company in a week is a Poisson random variable N with mean 20, and the amounts of diﬀerent claims are independent exponentially distributed random variables with mean 800. Compute the variance of the total claim amount the company receives in a week....
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 '09
 SAMORODNITSKY
 Variance, Probability theory, var, insurance company, X

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