What is the conditional joint distribution

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Reference no: EM131811624

Question: Conditioning independent Poisson variables on their sum. Let N, be independent Poisson variables with parameters λ_i, Think of the N, as the number of Points of scatter in disjoint part of the plane with areas λ_iwhere the mean intensity is on point per unit area.

a) What is the conditional joint distribution of (N_i, , , ,, ,N_m) given N_i + . . .. +N_m = n?

b) Suppose now that N has Poisson (λ) distribution, and given N = n the conditional joint distribution of some m-tuple of random variables (N_i, . .. N_m) is exactly what you found in part a). What can you conclude about the unconditional distribution of (N_i.. .. N_m)?

Reference no: EM131811624

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