Let X∼Poisson(λ)X \sim \text{Poisson}(\lambda)X∼Poisson(λ). Given that X≥1X \ge 1X≥1, what is the conditional expected value E[X∣X≥1]E[X \mid X \ge 1]E[X∣X≥1]?
λ1−e−λ\frac{\lambda}{1 - e^{-\lambda}}1−e−λλ
λe−λ\frac{\lambda}{e^{-\lambda}}e−λλ
λ+1\lambda + 1λ+1
λ−e−λ1−e−λ\frac{\lambda - e^{-\lambda}}{1 - e^{-\lambda}}1−e−λλ−e−λ