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
Famous quotes containing the words absolutely and/or continuous:
“The first duty of a conscientious person is to have his or her conscience absolutely under his or her own control.”
—Samuel Butler (18351902)
“There is no such thing as a life of passion any more than a continuous earthquake, or an eternal fever. Besides, who would ever shave themselves in such a state?”
—George Gordon Noel Byron (17881824)