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 .
Read more about this topic: Probability Density Function
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