Probability Density Function - Absolutely Continuous Univariate Distributions

Absolutely Continuous Univariate Distributions

A probability density function is most commonly associated with absolutely continuous univariate distributions. A random variable X has density f, where f is a non-negative Lebesgue-integrable function, if:

Hence, if F is the cumulative distribution function of X, then:

and (if f is continuous at x)

Intuitively, one can think of f(x) dx as being the probability of X falling within the infinitesimal interval .

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