BAN 001 Chapter Notes - Chapter 8: Abh, Probability Density Function, Probability Distribution
7 Sep 2016
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The uniform probability distribution is a widely used distribution in sampling and simulation. We study it because it is the most simple continuous probability distribution. Understanding the uniform distribution will help us greatly to understand other continuous distributions. The uniform distribution is: symmetric about it"s mean. Thus, its mean is equal to its median: characterized by two parameters, a and b. Figure 1 is a sketch of the uniform distribution. f(x) The mathematical formula for the uniform probability density. 1 b-a for a x b ; 0 otherwise. The mean, , and standard deviation, , of the uniform distribution are. = (a+b)/2 and = (b-a)/ 12 : the uniform distribution is an example of a continuous distribution. For all continuous distributions, probability is defined as an area over a given range, for example p(x1 x x2). Therefore, a critical characteristic of all continuous distributions is that probability is not defined for a specific value, say p(x=x1).
