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Random Variableshard
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Given XXX and YYY are independent random variables where X∼Poisson(2)X \sim \text{Poisson}(2)X∼Poisson(2) and Y∼Poisson(3)Y \sim \text{Poisson}(3)Y∼Poisson(3). Let Z=X+2YZ = X + 2YZ=X+2Y. What is Var(Z)Var(Z)Var(Z)?