## Continuous uniform distribution, Mathematics

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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 s2 = V(X) = (b - a)2/12

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