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An applet in which students enter the probability and amount of a payoff, then run many trials to see total payoff and average payoff per game.

Expected Value, Definition and Basic Properties

Definitions and Properties

This web page contains the definition of expected value for discrete and continuous random variables. It also defines moments and conditional expected value.

Expected Value, Definition and Basic Properties

Expected Value - Introduction

Wikipedia entry for expected value. It contains definitions for the finite, countable, and continuous cases; a discussion of properties; some uses and applications; and a brief history.

Expected Value, Definition and Basic Properties

Jensens Inequality - Video

A video explaining Jensen's Inequality to a general audience.

Expected Value, Inequalities

The Weak Law of Large Numbers - Video

A video lecture on convergence in probability, the Chebyshev inequality, and the Weak Law of Large Numbers.

Expected Value, Inequalities, Convergence Theorems, Law of Large Numbers

Chebyshev's Inequality and the Weak Law of Large Numbers for iid Two-Vectors - Simulation

A demonstration for two-dimensional random vectors of the Weak Law of Large Numbers. A circle represents the set of values within epsilon of the mean and a set of points is the random sample.

Expected Value, Inequalities, Convergence Theorems, Law of Large Numbers

Markov Chains

This webpage provides a very detailed and high-quality description of Markov Chains.

Stochastic Processes, Discrete Markov Chains

The Ehrenfest Chains

This webpage provides a very detailed and high-quality description of the Ehrenfest Chain as an example of a Markov Chain.

Stochastic Processes, Discrete Markov Chains, Probability

Basic Probability, conditional probability (Classroom Capsules and Notes)

This link takes you to the link of capsules in Basic Probability, Conditional Probability under Probability within Classroom Capsules and Notes.

Basic Probability, Conditional Probability, Probability

Stochastic processes, discrete Markov chains (Classroom Capsules and Notes)

This link takes you to the list of capsules in Stochastic Processes, Discrete Markov Chains under Probability within Classroom Capsules and Notes.