Using the provided routine random.f90 that generates an uniform random deviate in the [0,1) interval evaluate the integral

averaging over N random numbers uniformely distributed in the integration domain. Estimate the statistical error associated with this scheme.

Compute the same integral using a random variable that satisfies the probability distribution

and compare the obtained value for the statistical error with the previous case.

HINT: a simple way to generate a random variable with probability distribution is to define with uniformely distributed in the [0,1) interval.

Stefano de Gironcoli 2003-11-05