## Uniform Distribution

The discrete Uniform distribution is illustrated in Figure 2-4. The toss of the coin and the roll of the single die are discrete Uniform distributions. The principal attribute is that each value of the random variable has the same probability. In engineering, it is often useful to have a random number generator to simulate seemingly totally random events, each event being assigned a unique number. It is very much desired that the random numbers generated come from a discrete Uniform distribution so that no number, thus no event, is more likely than another.

Area = heighl (probability) x width (A value)

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If the random variable is continuous, or the values of the discrete random variable are so close together so as to be approximately continuous, then, like all continuous distributions, the vertical axis is scaled such that the "area under the curve" equals 1. Why so? This is just a graphical way of saying that if all probabilities for all values are integrated, then the total will come to 1.

where dX represents an increment on the horizontal axis and f(X) represents a value on the vertical axis. Vertical * horizontal = area. Thus, mathematical integration is an area calculation.