Uniform distribution, or rectangular distribution, is a distribution that has constant
probability over a fixed range. A random variable, *X*, is *uniform* on [a,b] if
*X* is equally likely to take any value in the range from *a* to *b*
(Exhibit 33.15).

*Notation: [a, b] means continuous values from a to b.*

The cumulative distribution function (cdf):

$$F(t)=\begin{cases}0 \,\,if \,\,t< a \\ \\ \frac{t-a}{b-a} \,\,if \,\,a \le t \le b \\ \\ 1 \,\,if \,\,t>b \end{cases}$$ $$E(X)= \frac{b-a}{2}, \,Var(X)=\frac{b-a}{12}$$*Use the Search Bar to find content on MarketingMind.*

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