Probability Density Functions

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Homework Statement


The number X is chosen at random between 0 and 1. Determine the probability density function of each of the random variables v=X/(1-X) and W=X(1-x).


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The Attempt at a Solution


The solution in the back of the book says "The random Variable V satisfies P(V< or = v) = P(X< or = v/(1+v)) = v/(1+v) for v > or = 0. Its density function is equal to 1/((1+v)^2) for v>0 and 0 otherwise. The random variable W satisfies P(W < or = w) = 1-sqrt(1-4w) for 0< or = w< or = (1/4) and its density function is equal to 2(1-4w)^(-1/2) for 0<w<(1/4) and 0 otherwise. Can someone walk me through the steps to get to this solution?
 

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