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Question

The variance of the data:

x:
1
a
a2
......
an
f:
nC0
nC1
nC2
......
nCn
is

A
(1+a22)n(1+a2)n
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B
(1+a22)n(1+a2)2n
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C
(1+a2)2n(1+a22)n
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D
none of these
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Solution

The correct option is B (1+a22)n(1+a2)2n
¯X=fixifi=nC0+a.nC1+a2.nC2+....an.nCnnC0+nC1+nC2+....nCn=(1+a)n2n
.
S.D.= fixi2fi(fixifi)2= nC0+a2.nC1+a4.nC2+....a2n.nCnnC0+nC1+nC2+....nCn[(1+a)n2n]2(1+a2)n2n(1+a2)2n

Variance=(S.D)2

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