Estimation of probability density function

estimation of probability density function

X is defined as a random variable which is uniformly distributed over (0, 1). In other form, it will be written like X~Unif(0,1).
In the other side Y is a new random variable which is defined as a function of X. That Y=-ln(X).
After that, estimate and plot the probability density function of Y. Find an analytical model that seems to fit estimated PDF.