Discrete Distributions
For discrete random variables, the conditional probability mass function of Y given (the occurrence of) the value x of X, can be written, using the definition of conditional probability, as:
As seen from the definition, and due to its occurrence, it is necessary that
The relation with the probability distribution of X given Y is:
Read more about this topic: Conditional Probability Distribution
Famous quotes containing the word discrete:
“One can describe a landscape in many different words and sentences, but one would not normally cut up a picture of a landscape and rearrange it in different patterns in order to describe it in different ways. Because a photograph is not composed of discrete units strung out in a linear row of meaningful pieces, we do not understand it by looking at one element after another in a set sequence. The photograph is understood in one act of seeing; it is perceived in a gestalt.”
—Joshua Meyrowitz, U.S. educator, media critic. “The Blurring of Public and Private Behaviors,” No Sense of Place: The Impact of Electronic Media on Social Behavior, Oxford University Press (1985)