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Question

For a Poission distribution, which of the following is true

A
Mean=Mode
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B
Median=S.D.
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C
Mean=Variance
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D
Median=Variance
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Solution

The correct option is C Mean=Variance
For Poission distribution we have P(r)=eπλrri(r=0,1,2,...)
mean =fixifi=r=0rP(r),fiP(r)=1=0+λeλ+2λ2eλ2!+3λ3eλ3!+..... =λeλ(1+λ11+λ22!+λ33!+.....)=λeλ.eλ=λ
similarly, o2= Variance =r=0r2P(r)(r=0rP(r))2 =λeλ(eλ+λeλ)λ2=λ= mean
mean=variance

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