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Question

If X is a random poisson variate such that α=p(X=1)=p(X=2), then p(X=4)=

A
2α
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B
α3
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C
αe2
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D
αe2
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Solution

The correct option is B α3
In Poisson distribution such that α=p(X=1)=p(X=2)
p(x;μ)=eμμxx!
=> α=eμμ11!=eμμ22! => α=eμμ
=> eμμ=eμμ22
=> μ=2
p(4;μ)=eμμ44!=eμμ×μ324=α×2324=α3

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