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Lecture

Random Variables: Expectation and Independence

In course

COM-302: Principles of digital communications

This course is on the foundations of digital communication. The focus is on the transmission problem (rather than being on source coding). ...

Description

This lecture covers the concepts of random variables, expectation, and independence. Emre Telatar explains how to compute expectations, the cumulative distribution function, and the notion of independence between random variables.

Instructor

Emre Telatar

I. Emre Telatar received the B.Sc. degree in electrical engineering from the Middle East Technical University, Ankara, Turkey, in 1986. He received the S.M. and Ph.D. degrees in electrical engineering and computer science from the Massachusetts Institute of Technology, Cambridge, in 1988 and 1992 respectively. In 1992, he joined the Communications Analysis Research Department at AT&T Bell Laboratories (later Lucent Technologies), Murray Hill, NJ. He has been at the EPFL since 2000. Emre Telatar was the recipient of the IEEE Information Theory Society Paper Award in 2001. He was a program co-chair for the IEEE International Symposium on Information Theory in 2002, and associate editor for Shannon Theory for the IEEE Information Theory Transactions from 2001 to 2004. He was awarded the EPFL Agepoly teaching prize in 2005. Emre Telatar's research interests are in communication and information theories.

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (32)

Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.

Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.

Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.

Convergence of random variables

In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied.

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