Suppose that X has a Poisson distribution. If $P(X = 2) = \frac{2}{3}P(X = 1)$, evaluate $P(X = 0)$.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $e^{-4/3}$
Given $P(X = 2) =\frac{2}{3} P(X = 1)$
$⇒\frac{e^{-λ}λ^2}{2!}=\frac{2}{3}\frac{e^{-λ}λ}{1!}⇒\frac{4}{3}$
Hence, $P(X = 0) = e^{-λ} = e^{-4/3}$.