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# In a poisson distribution if $P(X=2)=P(X=3)$ then the value of its parameter $\lambda$ is

$\begin{array}{1 1}(1)6&(2)2\\(3)3&(4)0\end{array}$

$P(X=x)=\large\frac{e^{- \lambda } \lambda^x}{x!}$
$P(X=2)=\large\frac{e^{- \lambda } \lambda^2}{2!}$
$P(X=3)=\large\frac{e^{- \lambda } \lambda^3}{3!}$
$P(X=2) =P(X=3)$
$\large\frac{e^{- \lambda } \lambda^2}{2!}=\large\frac{e^{- \lambda } \lambda^3}{3!}$
$\large\frac{1}{1.2} =\frac{\lambda}{1.2.3}$
=> $\lambda=3$
Hence 3 is the correct answer.