Uniform Distribution (discrete)
In probability theory and statistics, the discrete uniform distribution is a probability distribution whereby a finite number of equally spaced values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of equally spaced outcomes equally likely to happen".
If a random variable has any of possible values that are equally spaced and equally probable, then it has a discrete uniform distribution. The probability of any outcome is . A simple example of the discrete uniform distribution is throwing a fair die. The possible values of are 1, 2, 3, 4, 5, 6; and each time the die is thrown, the probability of a given score is 1/6. If two dice are thrown and their values added, the uniform distribution no longer fits since the values from 2 to 12 do not have equal probabilities.
The cumulative distribution function (CDF) of the discrete uniform distribution can be expressed in terms of a degenerate distribution as
where the Heaviside step function is the CDF of the degenerate distribution centered at, using the convention that
Read more about Uniform Distribution (discrete): Estimation of Maximum, Random Permutation
Famous quotes containing the words uniform and/or distribution:
“Odors from decaying food wafting through the air when the door is opened, colorful mold growing between a wet gym uniform and the damp carpet underneath, and the complete supply of bath towels scattered throughout the bedroom can become wonderful opportunities to help your teenager learn once again that the art of living in a community requires compromise, negotiation, and consensus.”
—Barbara Coloroso (20th century)
“My topic for Army reunions ... this summer: How to prepare for war in time of peace. Not by fortifications, by navies, or by standing armies. But by policies which will add to the happiness and the comfort of all our people and which will tend to the distribution of intelligence [and] wealth equally among all. Our strength is a contented and intelligent community.”
—Rutherford Birchard Hayes (1822–1893)