For a Poisson distribution X∼Poisson(λ)X \sim \text{Poisson}(\lambda)X∼Poisson(λ), what is the variance of Y=X2Y = X^2Y=X2?
λ2+λ\lambda^2 + \lambdaλ2+λ
4λ3+6λ2+λ4\lambda^3 + 6\lambda^2 + \lambda4λ3+6λ2+λ
λ4+2λ3+λ2\lambda^4 + 2\lambda^3 + \lambda^2λ4+2λ3+λ2
2λ2+λ2\lambda^2 + \lambda2λ2+λ