# Finding pdf of a random variable

7.9.1 Let Y1<Y2<Y3<Y4 denote the order statistics of a random sample of size n=4 from a distribution having pdf f(x;θ)= 1/θ, 0<x<θ, zero elsewhere, where 0<θ<infinity. Show that the pdf is of the form 1/θ f(x/θ), where f(w)=1, 0<w<1, zero elsewhere.

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#### Solution Summary

The solution contains detailed explanation of finding probability density function (pdf) of a random variable.

Transformations of Continuous Random Variables

Fully formatted problems can be found in the attached Word document.

1) Let X have the p.d.f. f(x) = 4x^3 , 0<x<1

Find the p.d.f. of Y = X^2

2) Let x have a gamma distribution with =3 and  = 2

determine the p.d.f. of Y=X^2.

3) The P.d.f. of X is f(x) =  x^(-1), 0<x<1 , 0<<. Let Y=-2 lnX. How is Y distributed?

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