Given X∼Poisson(λ)X \sim \text{Poisson}(\lambda)X∼Poisson(λ), evaluate the variance of the random variable W=1X+1W = \frac{1}{X+1}W=X+11.
1−e−λ(1+λ)λ2\frac{1 - e^{-\lambda}(1+\lambda)}{\lambda^2}λ21−e−λ(1+λ)
1−e−λλ−(1−e−λλ)2\frac{1 - e^{-\lambda}}{\lambda} - (\frac{1 - e^{-\lambda}}{\lambda})^2λ1−e−λ−(λ1−e−λ)2
e−λλ\frac{e^{-\lambda}}{\lambda}λe−λ
Var(W)Var(W)Var(W) does not exist