Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Transformations of Joint Densities

In course

MATH-232: Probability and statistics (for IC)

Cours d'introduction à la théorie des probabilités et aux statistiques. ...

Description

This lecture covers the transformations of joint continuous densities, including finding the marginal and conditional distributions, calculating the joint density of transformed random variables, and understanding the implications of transformations on probability distributions.

Instructors (2)

Emmanuel Abbé

Raphaël Jean Berthier

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Mathematics

Probability theory: Topics in probability theory

Related concepts (32)

Conditional probability

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(AB) or occasionally P_B(A).

Conditional probability distribution

In probability theory and statistics, given two jointly distributed random variables and , the conditional probability distribution of given is the probability distribution of when is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value of as a parameter. When both and are categorical variables, a conditional probability table is typically used to represent the conditional probability.

Bayesian probability

Bayesian probability (ˈbeɪziən or ˈbeɪʒən ) is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown.

Probability interpretations

The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical, tendency of something to occur, or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory. There are two broad categories of probability interpretations which can be called "physical" and "evidential" probabilities.

Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.

Related lectures (39)

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Probability Theory: Midterm Solutions

Covers the solutions to the midterm exam of a Probability Theory course, including calculations of probabilities and expectations.

Probability and Statistics

Covers probability distributions, moments, and continuous random variables.