**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Random Vectors and Stochastic Models for Communications

Description

This lecture covers random vectors, stochastic models for communications, joint cumulative distribution function, joint probability density function, marginal probability density function, conditional probability density function, independence of random variables, linear functions of two random variables, covariance, characteristic function, conditional probability, and expectation.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Instructor

Related concepts (46)

In course

COM-300: Stochastic models in communication

L'objectif de ce cours est la maitrise des outils des processus stochastiques utiles pour un ingénieur travaillant dans les domaines des systèmes de communication, de la science des données et de l'i

Μ operator

In computability theory, the μ-operator, minimization operator, or unbounded search operator searches for the least natural number with a given property. Adding the μ-operator to the primitive recursive functions makes it possible to define all computable functions. Suppose that R(y, x1, ..., xk) is a fixed (k+1)-ary relation on the natural numbers. The μ-operator "μy", in either the unbounded or bounded form, is a "number theoretic function" defined from the natural numbers to the natural numbers.

General recursive function

In mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense – as well as in a formal one. If the function is total, it is also called a total recursive function (sometimes shortened to recursive function). In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines (this is one of the theorems that supports the Church–Turing thesis).

Teaching assistant

A teaching assistant or teacher's aide (TA) or education assistant (EA) or team teacher (TT) is an individual who assists a teacher with instructional responsibilities. TAs include graduate teaching assistants (GTAs), who are graduate students; undergraduate teaching assistants (UTAs), who are undergraduate students; secondary school TAs, who are either high school students or adults; and elementary school TAs, who are adults (also known as paraprofessional educators or teacher's aides).

Characteristic function (probability theory)

In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the characteristic function is the Fourier transform of the probability density function. Thus it provides an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.

Joint probability distribution

Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal distributions, i.e. the distributions of each of the individual random variables. It also encodes the conditional probability distributions, which deal with how the outputs of one random variable are distributed when given information on the outputs of the other random variable(s).

Related lectures (44)

Random Vectors: Stochastic Models for CommunicationsCOM-300: Stochastic models in communication

Covers random vectors, joint probability, and Gaussian random variables in communication models.

Stochastic Models for CommunicationsCOM-300: Stochastic models in communication

Covers random vectors, joint probability density, independent random variables, functions of two random variables, and Gaussian random variables.

Probability and StatisticsMATH-232: Probability and statistics

Covers p-quantile, normal approximation, joint distributions, and exponential families in probability and statistics.

Linear Combinations: Moment-Generating FunctionsMATH-232: Probability and statistics

Explores moment-generating functions, linear combinations, and normality of random variables.

Probability Theory: Midterm SolutionsMATH-232: Probability and statistics

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