Home page for accesible maths 2.2 Review of Continuous random variables 2.2 Review of Continuous random variables 2.2.2 Exponential Distribution

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2.2.1 Uniform Distribution

The Uniform distribution is so called as the probability of any outcome is the same over an interval (a,b) and 0 outside the interval. Some properties of Uniform random variables include:

1.

Mean = $\frac{a+b}{2}$ .
2.

Variance = $\frac{(a-b)^{2}}{12}$ .
3.

PDF:

$f(x)=\left\{\begin{array}[]{ll}0,&x\leq a\\ \frac{1}{b-a},&x\in(a,b)\\ 0,&x\geq b.\end{array}\right.$
4.

CDF:

$F(x)=\left\{\begin{array}[]{ll}0,&x\leq a\\ \frac{x-a}{b-a},&x\in(a,b)\\ 1,&x\geq b.\end{array}\right.$