The *uniform distribution* is a continuous distribution that assigns only positive probabilities within a specified interval (*a*, *b*) — that is, all values between *a* and *b*. (*a* and *b* are two constants; they may be negative or positive.)

A continuous distribution can't be illustrated with a histogram, because this would require an *infinite* number of bars. Instead, a continuous distribution may be illustrated with a line or a curve. Areas under the line or the curve correspond to probabilities.

With the uniform distribution, all values over an interval (*a*, *b*) are equally likely to occur. As a result, the graph that illustrates this distribution is a *rectangle*. The figure shows the uniform distribution defined over the interval (0, 10).

The horizontal axis shows the range of values for *X* (0 to 10). The distribution assigns a probability of 0 to any value of *X* outside of the interval from 0 to 10.

The *width* of this interval equals the upper limit (*b*) minus the lower limit (*a*), which equals *b* – *a*. So in the figure, the width equals 10 – 0 = 10. The width of this interval represents the *base* of the rectangle. The *height* of the rectangle equals 1 divided by the base (1/10 in this case). The height always equals 1 divided by the base; this ensures that the area of the rectangle always equals 1. Areas under this rectangle represent probabilities. The total probability for any distribution is 1; therefore, the area under the rectangle must equal 1.

The area of a rectangle equals the base times the height, or in mathematical terms,