FM5002-HW12-5.2.12

D fin d 0 2 a the gen erating fun ction is 04 z b

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Unformatted text preview: Α ’’’ 0 23 0.4 0 0.4 3 0.2 e 3 0.2 4 4 is 2s 0.4 e 0.4 0.2 e 4 s . 9.6. 9.6. , Β’’’ s 3.2 i e 2 i s 12.8 e 4 is , so that Β’’’ 0 9.6 i. 0059− . Let X be a binary PCRV such that Pr[X = a] = p an d Pr[X = b] = q, where p + q = 1. Let f (t) be the Fourier transform of the 7 distribution of X. Assume E X 0 that is, p a Compute lim f t n n n bq 0. Assume SD X pa pe bq i ta qe itb an d f t n 0, an d observe that sin ce 2 pq b 14 a Then lim f t n n that is, pq b a 0.5. . The generatin g fun ction for the distribution of Xis p z a so f t 0.5 pa bq 2 n pe q i ta a pq b a2 p p q zb , qe q itb n n 1 2, b2 q p n . Recall that p q a2 p p b2 q q a2 p 1, b2 q . n i ta 2 lim p e i ta n n lim p n q qe it n itb n it a lim p 1 n ap bq t2 2n n n n 2 32 pa qb 2 On 32 lim 1 n q1 t2 8n n n On n 2 n itb 2 it b 2 n On 32 On 32 t2 e 8 . 0060− . Let X represent the price, three months from now, of some fin ancial asset. Assume that the expected an nual return is 1 2 %. (That is, if you in vest $1 in the asset today, then its expected value, one year from today, is $1 .02.) Assume that 1.02 is the expon en...
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