# Cumulative Density Function

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A Cumulative Density Function is a non-decreasing right-continuous unit function that returns the probability that a real-valued random variable *X* (with a given probability distribution) will be found at a value less than or equal to x

**AKA:**CDF, Cumulative Continuous Probability, Cumulative Distribution Function.**Example(s):****Counter-Example(s):****See:**Continuous Random Variable, CDF Function Estimation.

## References

### 2013

- http://en.wikipedia.org/wiki/Cumulative_distribution_function
- In probability theory and statistics, the
**cumulative distribution function**(**CDF**), or just distribution function, describes the probability that a real-valued random variable*X*with a given probability distribution will be found at a value less than or equal to x*. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to*x*. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.*

- In probability theory and statistics, the

### 2006

- (Dubnicka, 2006c) ⇒ Suzanne R. Dubnicka. (2006). “Random Variables - STAT 510: Handout 3." Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
- TERMINOLOGY : The cumulative distribution function (cdf) of a random variable X, denoted by FX(x), is given by FX(x) = P(X x), for all x 2 R.
- ALTERNATE DEFINITION: A random variable is said to be continuous if its cdf FX(x) is a continuous function of x.
- TERMINOLOGY : Let X be a continuous random variable with cdf FX(x). The probability density function (pdf) for X, denoted by fX(x), is given by fX(x) = d/dx FX(x),