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 a review of questions 1#-10#.
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 lecture includes the following topics: Bases and vectorspaces; Matrices and linear transfs.
This lecture includes the following topics: Bases; Matrices.
This lecture includes the following topics: Eigenvalues and eigenvectors.
This lecture includes the following topics: Review for midterm; Orthogonal group.
This lecture includes the following topics: Orthogonal group & geometry.
This lecture includes the following topics: Finite groups of motions.
This lecture includes the following topics: Discrete groups of motions.