Let X∼Poisson(λ)X \sim \text{Poisson}(\lambda)X∼Poisson(λ). What is the variance of Y=X2Y = X^2Y=X2?
λ4+2λ3+λ\lambda^4 + 2\lambda^3 + \lambdaλ4+2λ3+λ
λ2+2λ3\lambda^2 + 2\lambda^3λ2+2λ3
λ2+4λ3\lambda^2 + 4\lambda^3λ2+4λ3
λ+4λ2+2λ3\lambda + 4\lambda^2 + 2\lambda^3λ+4λ2+2λ3