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A continuous random variable has probability density function f(x)=6(xx)2,0xi, Find (i) mean (ii) variance.
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Mean = E (x)

=x.f(x).dx

=10x.6(xx2)dx=610(x2x3)dx=6[x33x44]10=6[(133144)(00)]=0.5ConsiderE(x2)=x2.f(x)dx=10x2.6(xx2)dx=610[x3x4]dx=6[x44x55]10=6[(144155)(00)]=0.3

Variance =E(x2)[E(x)]2=0.30.52=0.05

Hence, Mean =0.5 and …

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