The variance of Poisson distribution is 1. Then the probability that Poisson random variable X, takes the value equal to 2 is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{1}{2e}$
The probability mass function (PMF) is,
$P(X=k)=\frac{λ^ke^{-λ}}{k!}$
Substitute $λ=1,k=2$
$P(X=2)=\frac{1^2e^{-1}}{2!}=\frac{1}{2e}$