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6. Let N be the number of aerosol particles in a given volume of air. If...

6. Let N be the number of aerosol particles in a given volume of air. If the mean number M is a known constant, then it may be assumed that N has a Poisson distribution. However, M is random and follows a gamma Γ(n, λ) law. Using conditional expectation, or otherwise, determine the probability generating function of N, and hence identify its distribution.

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TOPIC:Conditional expectation and probability generating function.

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