Let X∼Poisson(λ)X \sim \text{Poisson}(\lambda)X∼Poisson(λ). Determine the expected value of the random variable 1X+1\frac{1}{X+1}X+11.
1−e−λλ\frac{1 - e^{-\lambda}}{\lambda}λ1−e−λ
e−λλ\frac{e^{-\lambda}}{\lambda}λe−λ
1λ+1\frac{1}{\lambda + 1}λ+11
eλ−1λ\frac{e^{\lambda} - 1}{\lambda}λeλ−1