✓ A sequence of random numbers R1, R2, RR3......... must have two important properties.
i) Uniformity i.e. they are equally probable everywhere.
ii) Independence, i.e. the current value of a random variable has no relation with previous values.
✓ Each Random Number Ri is an independent sample drawn from a continuous uniform distribution between zero and one.
- pdf f(x) =
- expectation E(R) =
- variance V(R) =
✓ Some consequences of the uniformity and independence properties.
i) 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.
ii) The probability of observing a value in a particular interval is independent of the previous values drawn.
