Question: Given u, y is Poisson with E(y u) = u????, where u is a positive random variable with E(u) = 1 and var(u) =

Given u, y is Poisson with E(y ∣ u) = u????, where u is a positive random variable with E(u) = 1 and var(u) = ????. Show that E(y) = ???? and var(y) = ???? + ????????2.

Explain how you can formulate the negative binomial distribution and a negative binomial GLM using this construction.

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