Continues 18.100. Roughly half the subject devoted to the theory of the Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals.

Learn how to make waves of all different shapes by adding up sines or cosines. Make waves in space and time and measure their wavelengths and periods. See how changing the amplitudes of different harmonics changes the waves. Compare different mathematical expressions for your waves.

In this math activity, learners practice decision-making skills leading to a better understanding of choice versus chance and building the foundation of mathematical probability. SKUNK is a variation on a dice game also known as "pig" or "hold'em." The object of SKUNK is to accumulate points by rolling dice. Points are accumulated by making several "good" rolls in a row but choosing to stop before a "bad" roll comes and wipes out all the points. SKUNK can be played by groups, by the whole class at once, or by individuals.

In this video segment from Cyberchase, the CyberSquad determines the fairness of a game in which there are three shapes distributed equally on nine squares. ***Access to Teacher's Domain content now requires free login to PBS Learning Media.

This lecture includes the following topics: Tartan Dice; Terminated Geometric; World Series Pitchers; Negative Hypergeometric; Coin Tossing.

This lecture includes the following topics: Casino Night; Random Walk Examples; Random Walk Terminology; Gambler's Ruin; Ruin in Fair Casino; Time until Win or Ruin; A Fair Game; Walk as a Random Variable; Ballot Theorem; Hitting Time Theorem; Expected Lead Times.

This lecture includes the following topics: Expected Lead Time; Bijections between Paths; Another Bijection; Last Visit to Origin; First Visit to Final; First Visit to Max; First Return; Returning Just Once; Strange but True.

This lecture includes the following topics: First Visit to Max; Sojourn Times; Independent Variables; Uncorrelated Variables: A Counterexample; Generating Function; Product of Gen Functions; A Simple Example; Gen Function for 2 Dice; Clever Loaded Dice; Well-Known Distributions.

This lecture includes the following topics: Basic Inequality; Markov's Inequality; Chebyshov's Inequality; Weak Law of Large Numbers; Weak Law, continued; Strong Law of Large Numbers

This lecture includes the following topics:Probability by Symmetry; Probability by Experiment; Payoffs and Probability; Fair Price and Probability; Notation to Combine Sets; Venn Diagrams; Events and Sample Spaces; Event Spaces; Addition of Probabilities; Probability Functions; Inclusion-Exclusion Rule; Many Ways to Skin a Cat

This lecture includes the following topics: Review of the Basics; DeMorgan's Laws; Inclusion-Exclusion; Cups and Saucers; Cups and Saucers # 2; Urns; Family Planning; Twenty-first-Century Sheherezade; Craps; Achilles Rolls of a 6

This lecture includes the following topics: Count A Cartesian Product; Principles of Counting; The Binomial Theorem; Counting Poker Hands; Counting Bridge Hands; The Munchkin Problem; Genoese Lottery; Counting Suit Patterns; Negative Binomial Theorem; Count by Inclusion-Exclusion.

This lecture includes the following topics: St. Paul at Lystra; Conditional Four Aces; Conditional Probability; Independence of Events; Complimentary Events; The Bearded Man Problem; Lemons; Two Useful Theorems; Conditional Munchkins; Monty Hall Problem; Random Desserts

This lecture includes the following topics: Conditional Craps; Independence of 3 Events; Compound Experiments; Accidental Independence; Sudden Death; Sampling Paradox.

This lecture includes the following topics: Wisdom of Solomon; Eddington's Controversy; Affirmative Action; Simpson's Paradox.

This lecture includes the following topics: Discrete Random Variables; Event Space for a DRV; Bridge and Poker; Binomial Distribution; Geometric Distribution; Negative Binomial Distribution; Exponential Function; Poisson Distribution; Distribution Function; Distribution Examples; Function of Random Var; First Computer Project.

This lecture includes the following topics: Expectation; Unconscious Statistician; Properties of Expectation; Binomial Expectation; Tail-Sum Theorem; Geometric Tail-Sum; Negative Binomial Expectation; Coupons Problem; Variance; Telescoping Series.

This lecture includes the following topics: Infinite Expectation; Royal Oak Lottery; Poisson as Limit; Conditional Random Var; Conditional Expectation; Runs of Heads and Tails; Two Wins Takes All.

This is a really nice task as it is open to everyone, can be solved in different ways and can also extend to work in combinatorics – a nice way of organizing counting. Ask students to work on this task in groups, and to display their results on posters. Often we name students' different approaches and strategies.