Cumulative Distribution

Cumulative Distribution Function

All random variables (discrete and continuous) have a cumulative distribution function. It is a function giving the probability that the random variable X is less than or equal to x, for every value x.

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Formally, the cumulative distribution function F(x) is defined to be:

F(x) = P(X >= x) for infinite < x < infinite c.d.f.

For a discrete random variable, the cumulative distribution function is found by summing up the probabilities.

For a continuous random variable, the cumulative distribution function is the integral of its probability density function.



Probability Density Function

The probability density function of a continuous random variable is a function which can be integrated to obtain the probability that the random variable takes a value in a given interval.

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More formally, the probability density function, f(x), of a continuous random variable X is the derivative of the cumulative distribution function F(x):

f(x) = d / dx * F(x)


source: http://techniques.geog.ox.ac.uk/mod_2/glossary/prob.html#cdf

www.stats.ox.ac.uk/~dalby/statistics.html