Explore a comprehensive 6-hour tutorial on combinatorial results and probability theory. Delve into topics such as N choose k, n balls into k cells, Vandermonde's Identity, and the Birthday Problem. Learn how to calculate probabilities for various scenarios involving coins, dice, cards, and boxes. Discover practical applications through examples like poker hand probabilities, Farkle dice game, and the Kansas Keno lottery. Gain insights into discrete order statistics, hypergeometric distributions, and Catalan numbers. Use R software for exact probability calculations and simulations. Analyze real-world problems, including Lewis Carroll's Pillow Problem and the probability of reaching diagonal points in random walks.
Overview
Syllabus
Combinatorial Results: N choose k.
Combinatorial Results: n balls into k cells.
Combinatorial Results: Probability of exactly m events.
Vandermonde's Identity.
How to Derive Poker Hand Probabilities.
Calculating Farkle Probabilities - Dice Rolling Game.
Using R to Calculate Exact Farkle Probabilities - Dice Rolling Game.
Birthday Problem / Paradox.
Probabilities with Coins.
Probabilities with Dice.
Probabilities with Cards.
Probabilities with Boxes (part 1/2).
Probabilities with Boxes (part 2/2).
Probabilities Miscellaneous.
Derivation for Numberphile - Lewis Carroll's Pillow Problem.
Example using Vandermonde's Identity: Sum of 2 Binomial Random Variables w/ Equal p..
Where is the 4th Ace in a Shuffled Deck? (part 1/2).
Where is the 4th Ace in a Shuffled Deck? (part 2/2).
SOA Exam P Sample Problem 265 (part 1/2): Sample without Replacement.
SOA Exam P Sample Problem 265 (part 2/2): Discrete Order Statistics.
Keno Lottery (1/6): Prove that the number of matches follows a Hypergeometric Distribution.
Keno Lottery (2/6): Should the Multiplier be used?.
Keno Lottery (3/6): Is the extra cost of Bulls-eye worth it?.
Keno Lottery (4/6): Average Award for Double Bulls-eye.
Keno Lottery (5/6): R Software Calculations and Simulations.
Keno Lottery (6/6): I need your help confirming or refuting the derivations!.
Probability of ever reaching a diagonal point in a random walk. Catalan Numbers. Pascal's Triangle..
Errors on the Kansas Keno Lottery Brochure.
Taught by
statisticsmatt
