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Unformatted text preview: Given that f Y ( Y ) = 2 &ye & &y 2 for y > , the mean of Y is E ( Y ) = 2 & Z 1 y 2 e & &y 2 dy (by letting u = &y 2 and du = 2 &ydy ) = 1 & 1 = 2 Z 1 u 1 = 2 e & u du = 1 & 1 = 2 & & 3 2 ± = 1 & 1 = 2 & 1 2 ± & & 1 2 ± = 1 2 r ± & : To obtain the variance of Y , we need E ( Y 2 ) E ( Y 2 ) = 2 & Z 1 y 3 e & &y 2 dy = Z 1 ² u & ³ e & u du = 1 & &(2) = 1 & : Hence, the variance of Y is V ar ( Y ) = E ( Y 2 ) & [ E ( Y )] 2 = 1 & & ± 4 & = 1 & ² 1 & ± 4 ³ : Question 4 Let Y be the mileage (in thousands of miles) that car owners get with a certain kind of radial tire. Then, Y ± Exp ( ² = 1 = 40) : (a) P ( Y ² 20) = Z 1 20 1 40 e & x 40 dx = ´ & e & x 40 µ 1 20 = e & 1 = 2 2 = 0 : 6065 : (b) P ( Y & 30) = Z 30 1 40 e & x 40 dx = & ± e & x 40 ± 30 = 1 ± e & 3 4 = 0 : 5276 : 3...
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This note was uploaded on 09/06/2010 for the course STAT STAT1306 taught by Professor Prof during the Fall '08 term at HKU.
 Fall '08
 Prof
 Statistics, Probability

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