![cdf for uniform distribution cdf for uniform distribution](https://i.ytimg.com/vi/KfunVw-0AH0/maxresdefault.jpg)
Let X: Ω → R be a random variable defined on a probability space (Ω, P). Constant and almost surely constant random variables provide a way to deal with constant values in a probabilistic framework. This is technically different from an almost surely constant random variable, which may take other values, but only on events with probability zero. In probability theory, a constant random variable is a discrete random variable that takes a constant value, regardless of any event that occurs. The cumulative distribution function of the degenerate distribution is then: The probability mass function is given by: The degenerate distribution is localized at a point k 0 on the real line. While this distribution does not appear random in the everyday sense of the word, it does satisfy the definition of random variable. Examples include a two-headed coin and rolling a die whose sides all show the same number. In mathematics, a degenerate distribution is the probability distribution of a discrete random variable whose support consists of only one value. The horizontal axis is the index i of k i. The connecting lines do not indicate continuity.)ĬDF for k 0=0. (Note that the function is only defined at integer indices.