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Question

The mean of the values 0,1,2,.....,n having corresponding weight nC0,nC1,nC2,.....,nCn respectively, is?

A
2n(n+1)
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B
2n+1n(n+1)
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C
n+12
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D
n2
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Solution

The correct option is D n2
The solution mean is ¯x=01+1nC1+2nC2+3nC3+....+nnCn1+nC1+nC2+....+nCn

=nr=0rnCrnr=0nCr=nr=1rnrn1Cr1nr=0nCr

=nnr=1n1Cr1nr=0nCr

=n2n12n=n2

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