## The Uniform Distribution

As the name implies, the uniform distribution is ''flat'' over its entire range, as shown in Figure 11.2. The discrete case of the uniform distribution was discussed earlier in this chapter with respect to the toss of a die where all the probabilities are equal.

The uniform distribution shows up in the phase relationship when we are converting two independent normal distributions with the same variance from

(a) The density function

(b) The cumulative distribution function (CDF)

### Figure 11.2. The uniform distribution.

rectangular to polar coordinates. Such a case, applied, for example, to shooting at a bull's-eye, means that the shot is equally likely to be at any angle over the range zero to 2^ radians.

The mean value for the uniform distribution that has a range from a to b is (a + b)/2 and its variance is (b - a)2/12. We also have seen that adding two uniform random variables leads to a triangular distribution.

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