The Uniform Distribution
This page covers Uniform Distribution, Expectation and Variance, Proof of Expectation and Cumulative Distribution Function.
A continuous random variable X which has probability density function given by:
f(x) = 1 for a £ x £ b
b  a
(and f(x) = 0 if x is not between a and b) follows a uniform distribution with parameters a and b. We write X ~ U(a,b)
Remember that the area under the graph of the random variable must be equal to 1 (see continuous random variables).
Expectation and Variance
If X ~ U(a,b), then:

E(X) = ½ (a + b)

Var(X) = (1/12)(b  a)^{2}
Proof of Expectation
Cumulative Distribution Function
The cumulative distribution function can be found by integrating the p.d.f between 0 and t: