Continuous Uniform Distribution
Consider the interest earned on a bank deposit. Let X equal the value after the decimal point. (Assume no rounding off to the nearest paise.) For instance, if the interest = Rs.72.587, then X = 0.587.
X can take any value between 0 and up to but not including 1. We may assume that each value is equally likely. In which case, X is said to have a continuous Uniform Distribution.
Figure
The probability density function of a typical random variable is given by
Note that the area under the curve equals 1.
It can be shown:
m = E(X) = (a + b)/2
s^{2} = V(X) = (b - a)^{2}/12