FM5002-HW12-5.2.12

2 a 1 e 2x 9 e x2 2 2 c 1 2 1 e 2x 9 e 1 x2 2 7 e x e

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Unformatted text preview: 1 2Π e 2x 9 e e x2 2 1 e 2x 9 2 e x2 2 e 2x 9 e x2 2 x 2Π 2 log 2 9 2 2Π 1 e2 i x 9 xe 7 e 0 x2 2 3. xe 7 2. 2Π 1 x x2 2 2 x 2Π 2Π 1 e. x e 7. 2Π 2 2Π d. x2 2 e 2Π 2Π b. 7 e x e 2x 9 2e x2 2 x log 2 9 2 log 2 9 2 e x2 2 xe 7 log 2 92 2 2 log 2 9 2. 2Π 2e x2 2 x 2 2Π 1 e2 i x 9 e x2 2 xe 11 2. 2Π 0059− . Let X be a bin ary PCRV such that Pr[X = a] = p and Pr[X = b] = q, where p + q = 1. Let f (t) be the Fourier tran sform of 3 the distribution of X. a. Compute E X4 . b. Compute E X5 . c. Compute f (0). d. Compute f 4 (0). e. Compute f 5 (0). a. E X4 p a4 q b4 . b.E X5 pa5 q b 5. c. The generatin g function for the distribution of Xis p z a q z b , so that the Fourier tran sform is f t p e i a t q e i b t an d f 0 p d. f ’ t iae ia t p ibe ibt q, f ’’ t a2 e ia t p b2 e ibt q, q 1. FM5002−HW12−5.2.12.nb f3 t e. f 4 t i a3 e ia t a4 e i b3 e p ia t p ibt q, so that f ’’ 0 b4 e ibt q , so that f 5 t a4 p 3 b4 q. i a5 p i b 5 q. 0059− . Let X be a bin...
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This note was uploaded on 01/19/2014 for the course MATH 5002 taught by Professor Adams during the Spring '08 term at Minnesota.

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