FM5002-HW12-5.2.12

B fin d the fourier tran sform of the distribution of

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Unformatted text preview: ... Xn . n a. The gen erating fun ction of the distribution is 0.4 z b. The Fourier tran sform of the distribution is 0.4 e 2 it c. The Fourier transform of X1 X2 ... Xn is 0.4 e 2 0.4 0.4 2i t 0.2 z 4 . 0.2 e n 0.4 4 it . 0.2 e 4it n n n 0059− . Let X be a PCRV whose distribution satisfies : Pr[X = −2] = 0.4, Pr[X = 0] = 0.4, an d Pr[X = 4] = 0.2. 6 c4 r. 4 FM5002−HW12−5.2.12.nb The nth raw momen t of Xis E Xn . The momen t generatin g function is obtain ed from the gen erating fun ction after one replaces z by e s . Let Α s be the moment gen erating function of the distribution of X. Let Β s be the Fourier transform of the distribution of X. a. Fin d Α (s). b. Fin d Α’’’ (0). c. Find the third raw momen t of X. d. Fin d Β’’’ (0). 2 a. The gen erating fun ction is 0.4 z b. Α ’’’ s 3.2 e c. E X3 0.4 d. Β s 2s 0.4 e 2 i s 0.4 0.2 z 4 , so that the momen t gen eratin g function Α s 12.8 e 4 s , so that...
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