A random variable $X$ follows poisson distribution such that $P (X = k) = P (X = k + 1)$ then the parameter of the distribution $λ =$

K

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K + 1

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\frac{K}{2}

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\frac{K + 1}{2}

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Solution

The correct option is B $K + 1$
$P (X = k) = P (X = k + 1)$
$P (x; μ) = \frac{e^{- μ} μ^{x}}{x!}$

$P (k; μ) = \frac{e^{- μ} μ^{k}}{k!} = P (k + 1; μ) = \frac{e^{- μ} μ^{k + 1}}{(k + 1)!}$

$1 = \frac{μ}{k + 1}$

$μ = k + 1$

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