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please solve these problems 4. reciprocating gammas & the multivariate beta: Suppose that Zi inder G(pi), iEN and, for each n E N, set Sn

please solve these problems

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4. reciprocating gammas & the multivariate beta: Suppose that Zi inder G(pi), iEN and, for each n E N, set Sn = Z1+ . .. + Zn and Yn = Sn/ Sn+1. a) Prove that the Yn's are mutually statistically independent. b) Provide a joint probability density function for (Y1, . . ., Yn). c) For pi = 1, iEN and Xn = Yn. In, n EN obtain P(X1

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