This course covers learning outcomes related to combinatorial results, probability calculations, Vandermonde's Identity, deriving poker hand probabilities, calculating Farkle probabilities, and solving various probability problems using tools like R. The teaching method includes theoretical explanations, derivations, examples, and practical problem-solving. The intended audience for this course includes individuals interested in advanced probability theory, combinatorics, and probability calculations using different tools and techniques.
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
