Cumulative distribution function

CFA level I / Quantitative Methods: Application / Common Probability Distributions / Cumulative distribution function

A cumulative distribution function (cdf) specifies the probability that a random variable X is less than or equal to a particular value x. It can be specified as P(X≤x). The notation of the cumulative distribution function for both discrete and continuous variables is F(x) = P(X≤x).

It is called cumulative as it adds up (cumulates) all the probabilities of the random variable till the value x. To find F(x), we add up all the values of the probability function for all outcomes less than or equal to x. The function of the cdf is similar to the cumulative relative frequency that we discussed earlier.

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