For uniformly distributed real random numbers, , on [0,1), the average
value should be 0.5. Note that, to compute the mean and variance, we can order
the random numbers in any fashion (as both of these computations are
independent
of order). It is useful to choose to order the real, random numbers in
ascending order, and approximate the distribution in the form of a continuous
variable **R**. Verify by direct integration that the average, , and
the
variance, , should be 0.5 and 0.083333, respectively, as follows: