In mathematics, a degenerate distribution is the probability distribution of a random variable which only takes a single value. Examples include a two-headed coin and rolling a die whose sides all show the same number. While this distribution does not appear random in the everyday sense of the word, it does satisfy the definition of random variable.
The degenerate distribution is localized at a point k0 on the real line. The probability mass function is given by:
The cumulative distribution function of the degenerate distribution is then:
Read more about Degenerate Distribution: Constant Random Variable
Famous quotes containing the words degenerate and/or distribution:
“He was ... a degenerate gambler. That is, a man who gambled simply to gamble and must lose. As a hero who goes to war must die. Show me a gambler and I’ll show you a loser, show me a hero and I’ll show you a corpse.”
—Mario Puzo (b. 1920)
“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)