Search results
Results From The WOW.Com Content Network
The continuous uniform distribution with parameters = and =, i.e. (,), is called the standard uniform distribution. One interesting property of the standard uniform distribution is that if u 1 {\displaystyle u_{1}} has a standard uniform distribution, then so does 1 − u 1 . {\displaystyle 1-u_{1}.}
The uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely, is a special case of the four-parameter Beta distribution. The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
A beta distribution with shape parameters α = β = 1 is a continuous uniform distribution over the real numbers 0 to 1. A beta-binomial distribution with parameter n and shape parameters α = β = 1 is a discrete uniform distribution over the integers 0 to n.
It is the probability model for the outcomes of tossing a fair coin, rolling a fair die, etc. The univariate continuous uniform distribution on an interval [a, b] has the property that all sub-intervals of the same length are equally likely. Binomial distribution with normal approximation for n = 6 and p = 0.5
The uniform distribution on the interval [a,b] is the maximum entropy distribution among all continuous distributions which are supported in the interval [a, b], and thus the probability density is 0 outside of the interval.
Uniform distribution may refer to: Continuous uniform distribution; ... Toggle the table of contents. Uniform distribution.
This distribution for a = 0, b = 1 and c = 0.5—the mode (i.e., the peak) is exactly in the middle of the interval—corresponds to the distribution of the mean of two standard uniform variables, that is, the distribution of X = (X 1 + X 2) / 2, where X 1, X 2 are two independent random variables with standard uniform distribution in [0, 1]. [1]
That is, for any two random variables X 1, X 2, both have the same probability distribution if and only if =. [citation needed] If a random variable X has moments up to k-th order, then the characteristic function φ X is k times continuously differentiable on the entire real line.