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If a poisson variate $X$ satisfies $P(X=2)$ $=P(X=3)$, then $P(X=5)=$
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Verified Answer
The correct answer is:
$\frac{81}{40 e^3}$
According to given information,
$\frac{\lambda^2 e^{-\lambda}}{2 !}=\frac{\lambda^3 e^{-\lambda}}{3 !} \Rightarrow \lambda=3$
So, $P(X=5)=\frac{3^5 e^{-3}}{5 !}=\frac{81 e^{-3}}{40}=\frac{81}{40 e^3}$ Hence, option (b) is correct.
$\frac{\lambda^2 e^{-\lambda}}{2 !}=\frac{\lambda^3 e^{-\lambda}}{3 !} \Rightarrow \lambda=3$
So, $P(X=5)=\frac{3^5 e^{-3}}{5 !}=\frac{81 e^{-3}}{40}=\frac{81}{40 e^3}$ Hence, option (b) is correct.
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