If Y is uniformly distributed over the interval (0,1), i.e. f(y) = 1 for 0< y < 1.
Show that U = -2 loge(Y) has a negative exponential distribution. By comparing the density
functions or the moment generating functions, show also that an exponential distribution is
identical to a chi-square distribution with 2 degrees of freedom. If Y1, Y2, ..., Yn are
independently uniformly distributed over the interval (0,1), determine the distribution of
U = -2loge(Y1Y2...Yn) = summation(-2loge(Yi)).