# Cumulative distribution function

## Probability that random variable X is less than or equal to x / From Wikipedia, the free encyclopedia

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In probability theory and statistics, the **cumulative distribution function** (**CDF**) of a real-valued random variable , or just **distribution function** of , evaluated at , is the probability that will take a value less than or equal to .[1]

Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by a right-continuous monotone increasing function (a càdlàg function) satisfying and .

In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to . Cumulative distribution functions are also used to specify the distribution of multivariate random variables.