Finding PDF of uniform distribution

[electroissues]

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!

 

[lanedance]

so as its constant doesn't $f_X(x)=1$ in [0,1], zero otherwise

then use the fact that the probability for a given interval dx and corresponding interval dy must be the same
$$|f_X(x)dx| = |f_Y(y)dy|$$

 

[lanedance]

is that what you tried to do? can you show your working?