If X∼Poisson(λ)X \sim \text{Poisson}(\lambda)X∼Poisson(λ), what is the variance of Y=X2Y = X^2Y=X2?
λ\lambdaλ
λ+4λ2\lambda + 4\lambda^2λ+4λ2
λ2+2λ3\lambda^2 + 2\lambda^3λ2+2λ3
λ+3λ2\lambda + 3\lambda^2λ+3λ2