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Random Variableshard
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Suppose XXX and YYY are independent random variables where X∼Poisson(λ1)X \sim \text{Poisson}(\lambda_1)X∼Poisson(λ1​) and Y∼Poisson(λ2)Y \sim \text{Poisson}(\lambda_2)Y∼Poisson(λ2​). A researcher defines Z=X−YZ = X - YZ=X−Y. What is the characteristic function ϕZ(t)\phi_Z(t)ϕZ​(t)?