- A sequence of random numbers,
must have
two important properties:
- uniformity, i.e. they are equally probable every where
- independence, i.e. the current value of a random variable has no relation with the previous values

- Each random number is an independent sample drawn from a
continueous uniform distribution between zero and one.
- pdf

- expectation

- variance

- pdf
- Some consequences of the uniformity and independence
properties
- If the interval (0,1) is divided into
*n*sub-intervals of equal length, the expected number of observations in each interval is*N/n*where*N*is the total number of observations. Note that*N*has to be sufficiently large to show this trend. - The probability of observing a value in a particular interval is independent of the previous values drawn.

- If the interval (0,1) is divided into

Meng Xiannong 2002-10-18