Example
To continue with our motivating example above, we consider a real-valued random variable X and write
(where for the example given.) This limit, if it exists, is a regular conditional probability for X, restricted to
In any case, it is easy to see that this limit fails to exist for outside the support of X: since the support of a random variable is defined as the set of all points in its state space whose every neighborhood has positive probability, for every point outside the support of X (by definition) there will be an such that
Thus if X is distributed uniformly on it is truly meaningless to condition a probability on "".
Read more about this topic: Regular Conditional Probability
Famous quotes containing the word example:
“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)