A Poisson variable satisfies P(x = 1) = P(x = 2). Find P(x = 5).

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P(x = 1) = P(x = 2)

Yanam BieapBIEAP Intermediate Board 2022Subjective· 2mImportance★★★★★

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The parameter is $\lambda=2$ and $P(x=5)=\dfrac{4}{15e^{2}}\approx0.036$ .

For a Poisson variable, $P(x=k)=\dfrac{e^{-\lambda}\lambda^{k}}{k!}$ .

Given $P(x=1)=P(x=2)$ :

$e^{-\lambda}\lambda=\dfrac{e^{-\lambda}\lambda^{2}}{2}\Rightarrow 1=\dfrac{\lambda}{2}\Rightarrow \lambda=2.$

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Q.A Poisson variable satisfies $P(x = 1) = P(x = 2)$ . Find $P(x = 5)$ .