First slide

Random variable and probability distribution

Question

In a Poisson distribution $P (X = 0) = 2 P (X = 1)$ then the standard deviation =

Easy

A

$\frac{1}{2}$
B

$\frac{1}{\sqrt{2}}$
C

$\frac{1}{3}$
D

$\frac{1}{\sqrt{3}}$

Solution

$P (X = 0) = 2 P (X = 1)$ (Given)
$\Rightarrow \frac{e^{- λ} λ^{0}}{0!} = \frac{2 e^{- λ} λ^{1}}{1!}$

$\Rightarrow λ = \frac{1}{2}$

S.D $= \sqrt{λ} = \frac{1}{\sqrt{2}}$

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