If a random variable X follows Poisson distribution such that $3P(X=2)=2P(X=1)$, then the variance of X is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{4}{3}$
A Poisson-distributed random variable X is,
$P(X=k)=\frac{e^{-λ}λ^k}{k!}$ [λ = Variance]
and,
$3P(X=2)=2P(X=1)$
$3×\frac{e^{-λ}λ^2}{2!}=2×\frac{e^{-λ}λ^1}{1!}$
$⇒\frac{3λ^2}{2}=2λ$
$⇒λ(3λ-4)=0$
$⇒λ=\frac{4}{3}$