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Question

If a variable x takes values 0,1,2,....n with frequencies proportional to the binomial coefficients nC0,nC1,nC2,......nCn, then mean of distribution is

A
n(n+1)2
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B
n2
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C
2n
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D
n(n1)2
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Solution

The correct option is C 2n
Here, μ1=rnrn1Cr1nCr
=n.2n12n=n2
and
μ2=12nn0{(r1)+r}nCr
=12nn0r(r1)nCr+n2
=12nn0r(r1)n(n1)r(r1)n2Cr2+n2
=n(n1)2n.2n2+n2
=n(n1)4+n2
Variance σ2=μ2(μ1)2 =n(n1)4+n2(n2)2=n4

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