if a variable X takes values 0,1,2,.....n with frequencies nC0 , nC1,nC2 ,........., nCn then write variance X

x¯=i=0nxifii=0nfi=0×C0n+1×C1n+2×C2n+......+n×CnnC0n+C1n+C2n+......+Cnn

x¯=n×2n-12nn+1=nn+12

Variance(X), σ2=1ni=0nxi-x¯2

 σ2=1n0+1+2+......+n-nx¯2

 σ2=1nnn+12-n×nn+122

 σ2=1nnn+121-n2

σ2=n24nn+121-n2

σ2=n4n+12n-12
 

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