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Question

If variable takes values 0,1,2,......, n with frequencies qn. n1 qn−1 p , n(n−1)1.2 qn−2 p2..........,pn where p+q = 1, then the mean is

A
pq
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B
np
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C
nq
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D
np2
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Solution

The correct option is B np
Given variable takes values 0,1,2,......n
with frequencies qn,n1qn1.p,n(n1)1.2qn2p2,......pn

The frequencies are nC0qnp0, nC1qn1p1, nC2qn2p2....... nCrqnrp3,......., nCnq0pn

Sum of the frequencies are (p+q)n=1
now the combined sum is

0.( nC0qnp0)+1.( nC1qn1p1)+2( nC2qn2p2)+.......+r( nCrqnrpr)+....+n( nCrq0pn)
=nr=1r( nCrqnrpr)
=nr=1n(n1)!(nr)!(r1)!q(n1.(r1)pr1p
=npr1=0n (n1)C(r1)q(n1)(r1)pr1
=npnr1=0 n1Cr1qn1r1,pr1

=np(p+q)n1

=np

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