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Unformatted text preview: × 1 × . 02 + 200000 × . 5 × . 01 + 200000 × . 25 × . 1 = 200000(0 . 002 + 0 . 005 + 0 . 025) = 6400 Therefore, the insurance company should charge $6900(= $6400+$500) in order to obtain an average proﬁt of $500. 4.14 Solution: E ( X ) = Z ∞∞ xf ( x ) dx = Z 1 x 2( x + 2) 5 dx = Z 1 ± 2 5 x 2 + 4 5 x ² dx = ³ 2 15 x 3 + 2 5 x 2 ´ 1 = 8 15 4.17 Solution: μ g ( X ) = E [ g ( X )] = X x g ( x ) f ( x ) = g (3) f (3) + g (6) f (6) + g (9) f (9) = 25 × 1 6 + 169 × 1 2 + 361 × 1 3 = 209 2 4.20 Solution: μ g ( X ) = E [ g ( X )] = Z ∞∞ g ( x ) f ( x ) dx = Z ∞ g ( x ) f ( x ) dx = Z ∞ e 2 3 x ex dx = Z ∞ e1 3 x dx = h3 e1 3 x i ∞ = 3 3...
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 Fall '08
 Sally

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