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please solve the problem 7.8 For i = 1, ..., n let N, have a mixed Poisson distribution with parameter X. Let the mixing distribution

please solve the problem

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7.8 For i = 1, ..., n let N, have a mixed Poisson distribution with parameter X. Let the mixing distribution for N; have pgf Pi(z). Show that N = N1 + . .. + Nn has a mixed Poisson distribution and determine the pgf of the mixing distribution

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