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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]

Cumulative distribution function for the exponential distribution
Cumulative distribution function for the normal distribution

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.