# Uniform Distribution

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## uniform distribution

[′yü·nə‚fȯrm ‚di·strə′byü·shən]*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.

## Uniform Distribution

a special type of probability distribution of a random variable *X* that takes on values in the interval (*a - h, a + h)*. A uniform distribution is characterized by the probability density function

The mathematical expectation is *EX = a*, the variance is D *X= h ^{2}/3*, and the characteristic function is

By means of a linear transformation the interval (*a - h, a + h*) can be made to correspond to any given interval. Thus, the variable *Y = (X - a + h*)/2*h* is uniformly distributed over the interval (0, 1). Suppose the variables *Y*_{1}, *Y*_{2},.…, *Y*_{n} are uniformly distributed over the interval (0, 1). When their sum is normalized by the mathematical expectation *n/2* and the variance n/12, the distribution law of the normalized sum rapidly approaches a normal distribution as *n* increases. In fact, the approximation is often sufficient for practical applications even when *n* = 3.