Suppose that the variables X, Y, and Z are iid, each having the U(0,1) distribution. Calculate P(X > Y Z).

Let X and Y be independent Poisson variables, with X ∼ P(λ) and Y ∼ P(µ). As shown

in Example 4.3.2, X +Y ∼ P(λ + µ). Identify the conditional distribution of X, given

X +Y = n.

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