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If a variable takes values $0, 1, 2, \dots, n$ with frequencies $1,^{n} C_{1},^{n} C_{2}, \dots,^{n} C_{n}$ then the AM is

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Correct option is D

The required mean is given by X¯=0⋅1+1⋅nC1+2⋅nC2+3⋅nC3+…+n⋅nCn1+nC1+nC2+…+nCnX¯=∑r=0n r⋅nCr∑r=0n nCr=∑r=1n r⋅nrn−1Cr−1∑r=0n nCr=n∑r=1n n−1Cr−1∑r=0n nCrX¯=n×2n−12n=n2`

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Variate x	1	2	3	4	5
Frequency f of x	4	5	y	1	2

If a variable takes values 0,1,2,…,n with frequencies 1,nC1,nC2,…,nCn then the AM is

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If a variable takes values $0, 1, 2, \dots, n$ with frequencies $1,^{n} C_{1},^{n} C_{2}, \dots,^{n} C_{n}$ then the AM is