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Let X ∼ Poisson(µ1) and Y ∼ Poisson(µ2) be two independent random variables. Define Z =...

Let X ∼ Poisson(µ1) and Y ∼ Poisson(µ2) be two independent random variables.

Define Z = X +Y .

Show that X | Z = n ∼ Binomial( n, µ1 / (µ1 + µ2))

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