A random variable \( X \) follows Poisson distribution. The variance of \( X \) is 2. The value of \( P(X=3) \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{4}{3e^{2}} \)
For a Poisson distribution with parameter λ, mean = variance = λ. So λ = 2.
\( \displaystyle P(X=r)=\frac{e^{-\lambda}\lambda^{r}}{r!} \)
\( \displaystyle P(X=3)=\frac{e^{-2}\cdot 2^{3}}{3!} \)
\( \displaystyle =\frac{8}{6e^{2}}=\frac{4}{3e^{2}} \)