A Conditional Probability Mass Function

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The probability mass function of a pair of discrete random variables is the function . The conditional mass function of given is the function . Thus the mass function (left-hand plot) computes probabilities of intersections, while the conditional mass function (right-hand plot) computes conditional probabilities. For each value, the slice through the conditional mass function at that value gives the distribution of when assumes the value . The mean of this distribution is the conditional expectation of given , . The weighted average of the conditional expectations, with the weights given by the probability that is the expected value of .

[more]

You can reverse the roles of and to obtain the conditional mass function of given and the conditional expectation of given .

[less]

Contributed by: Chris Boucher (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

detailSectionParagraph


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send