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:
“Our brave forefathers have exterminated all the Indians, and their degenerate children no longer dwell in garrisoned houses nor hear any war-whoop in their path.”
—Henry David Thoreau (1817–1862)
“In this distribution of functions, the scholar is the delegated intellect. In the right state, he is, Man Thinking. In the degenerate state, when the victim of society, he tends to become a mere thinker, or, still worse, the parrot of other men’s thinking.”
—Ralph Waldo Emerson (1803–1882)