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:
“It was always the work that was the gyroscope in my life. I don’t know who could have lived with me. As an architect you’re absolutely devoured. A woman’s cast in a lot of roles and a man isn’t. I couldn’t be an architect and be a wife and mother.”
—Eleanore Kendall Pettersen (b. 1916)
“I can never get people to understand that poetry is the expression of excited passion, and that 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 (1788–1824)