Let X∼Poisson(λ)X \sim \text{Poisson}(\lambda)X∼Poisson(λ). What is P(X=k∣X≤1)P(X=k | X \le 1)P(X=k∣X≤1)?
11+λ\frac{1}{1+\lambda}1+λ1
λ1+λ\frac{\lambda}{1+\lambda}1+λλ
λkk!(1+λ)\frac{\lambda^k}{k!(1+\lambda)}k!(1+λ)λk
None of the above