Given X∼Poisson(λ)X \sim \text{Poisson}(\lambda)X∼Poisson(λ), consider the variable Y=(−1)XY = (-1)^XY=(−1)X. What is the expected value E[Y]E[Y]E[Y]?
e−λe^{-\lambda}e−λ
e−2λe^{-2\lambda}e−2λ
1−e−λ1 - e^{-\lambda}1−e−λ
e−λ/2e^{-\lambda/2}e−λ/2