Let 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) be independent random variables. Find the expected value of X(−1)YX(-1)^YX(−1)Y.
λ1e−2λ2\lambda_1 e^{-2\lambda_2}λ1e−2λ2
−λ1e−λ2-\lambda_1 e^{-\lambda_2}−λ1e−λ2
λ1e−λ2\lambda_1 e^{-\lambda_2}λ1e−λ2
0