Formal Definition
(This definition may be extended to any probability distribution using the measure-theoretic definition of probability.)
A random variable X with values in a measure space (usually Rn with the Borel sets as measurable subsets) has as probability distribution the measure X∗P on : the density of X with respect to a reference measure μ on is the Radon–Nikodym derivative:
That is, f is any measurable function with the property that:
for any measurable set .
Read more about this topic: Probability Density Function
Famous quotes containing the words formal and/or definition:
“There must be a profound recognition that parents are the first teachers and that education begins before formal schooling and is deeply rooted in the values, traditions, and norms of family and culture.”
—Sara Lawrence Lightfoot (20th century)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)