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Question

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

A
K
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B
K+1
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C
K2
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D
K+12
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Solution

The correct option is B K+1
P(X=k)=P(X=k+1)
P(x;μ)=eμμxx!

P(k;μ)=eμμkk!=P(k+1;μ)=eμμk+1(k+1)!

1=μk+1

μ=k+1

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