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Random Drawing Tool, Individual Trials - Simulation of Drawing Tickets

This applet simulates drawing numbered tickets from a box. The relative frequency of each number is displayed. The user can select the tickets which are placed in the box.

Randomizing Gadgets

Discrete - Time Markov Chains

This text-based web page provides Dr. W. Rolke's notes on Discrete Time Markov Chains. It provides an easy to follow description followed by common examples. Dr.

Stochastic Processes, Discrete Markov Chains

A Random Walk in One Dimension: Applet Demonstration

This applet constructs a histogram of the resulting path of a random walker in one dimension.

Stochastic Processes, Discrete Markov Chains

Chebyshev's Inequality - Introduction

Wikipedia entry for Chebyshev's Inequality. It contains statements and proofs for several forms. Also contains a discussion of ways to improve the bounds.

Expected Value, Inequalities

Jensen's Inequality - Introduction

Wikipedia entry for Jensen's Inequality. It contains statements and proofs for several forms, and applications including for a probability density function.

Expected Value, Inequalities

Expectation and Variance of a Random Variable - Video

This video lecture introduces the definition of expected value and does a discrete example.

Expected Value, Definition and Basic Properties, Expected Value, Variance and Higher Moments

This video lecture introduces the definition of expected value and does a discrete example. Then the definition of variance is given, and properties are discussed, including the variance of a linear function of a random variable.

Video from Khan Academy. An introduction to expected value. It starts with the arithmetic mean and develops expected value for a discrete distribution.

Expected Value, Definition and Basic Properties

Expected Value of Binomial Distribution - Video

Video from Khan Academy. Proves that the expected value of the binomial distribution is \(n*p\).

Expected Value, Definition and Basic Properties, Discrete Distributions, Bernoulli and Binomial

Expectation - Introduction

This web page contains the definition of expected value for discrete distributions, and also one example comparing two choices to show which has the largest expected value.

Expected Value, Definition and Basic Properties, Probability

Expected Value - Introductory Lesson Plan

A lesson plan for introducing the concept of expected value. Includes NCTM standards, student prerequisites, links to vocabulary, an outline of the lesson, and suggested follow-up.

Expected Value, Definition and Basic Properties, Probability