Consider X∼Poisson(λ)X \sim \text{Poisson}(\lambda)X∼Poisson(λ). What is the variance of the random variable Y=X2Y = X^2Y=X2?
λ2+λ\lambda^2 + \lambdaλ2+λ
λ4+6λ3+7λ2\lambda^4 + 6\lambda^3 + 7\lambda^2λ4+6λ3+7λ2
λ+4λ2+2λ3\lambda + 4\lambda^2 + 2\lambda^3λ+4λ2+2λ3
λ+3λ2+λ3\lambda + 3\lambda^2 + \lambda^3λ+3λ2+λ3