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## Homework Statement

Let X be a uniform random variable in the interval [0,1] i.e., X = U [(0,1)]. Then a new random variable Y is given by Y= g(X), where g(x)= -a. ln(x). Show that Y is exponentially distributed. What is the mean of Y?

## Homework Equations

fX(x) = 1/ lambda . exp (-x/ lambda)

0 otherwise

## The Attempt at a Solution

Y = g(X) can be computed via FY(y)= Summation 1/ differentiation of g(x) multiplied with Fx(x)

I can't show how this is exponential.

Please help!