4.1 Intro to Discrete Probability
- 4.1.1 Tree Model: Video
- 4.1.2 Socks and Shoes
- 4.1.3 Simplified Monty Hall Tree: Video
- 4.1.4 Simplify Prize Tree
- 4.1.5 Sample Spaces: Video
- 4.1.6 Sum Rule Practice
- 4.1.7 Addition Rule
- 4.1.8 Fun With Coins
4.2 Conditional Probability
- 4.2.1 Conditional Probability Definitions: Video
- 4.2.2 Dicey Sum
- 4.2.3 Law of Total Probability: Video
- 4.2.4 Cavities and Candy
- 4.2.5 Bayes' Theorem: Video
- 4.2.6 Two Boys
- 4.2.7 Monty Hall Problem: Video
- 4.2.8 Conditional Probability
- 4.2.9 Dicey Game
- 4.2.10 Watch Out For Crocodiles
4.3 Independence & Causality
- 4.3.1 Independence: Video
- 4.3.2 Independent Dice Rolls
- 4.3.3 Mutual Independence: Video
- 4.3.4 Mutually Independent Dice Rolls
- 4.3.5 Independent vs Disjoint
- 4.3.6 Labeled Balls
- 4.3.7 Paradox
4.4 Random Variables, Density Functions
- 4.4.1 Bigger Number Game: Video
- 4.4.2 Random Variables: Independence: Video
- 4.4.3 Odd Heads and Matches
- 4.4.4 Random Variables: Uniform & Binomial: Video
- 4.4.5 Late For A Date
- 4.4.6 A Random Number
- 4.4.7 PDF to CDF
- 4.4.8 Dice And Coin Game
4.5 Expectation
- 4.5.1 Expectation: Video
- 4.5.2 Uneven Dice
- 4.5.3 Expected Number Of Heads: Video
- 4.5.4 Expected Number of Heads
- 4.5.5 Total Expectation: Video
- 4.5.6 Another Dice and Coin Game
- 4.5.7 Mean Time to Failure: Video
- 4.5.8 Three Machines Failing
- 4.5.9 Linearity of Expectation: Video
- 4.5.10 Fair and Biased Coins
- 4.5.11 Binomial Board Breaking
- 4.5.12 Great Expectations
- 4.5.13 Expectation of a Uniform Distribution
4.6 Deviation: Markov & Chebyshev Bounds
- 4.6.1 Deviation From The Mean: Video
- 4.6.2 Don't Expect the Expectation
- 4.6.3 Markov Bounds: Video
- 4.6.4 Markov Bound
- 4.6.5 Chebyshev Bounds: Video
- 4.6.6 Inside the TA's Brain
- 4.6.7 Variance: Video
- 4.6.8 Practice with Variance
- 4.6.9 Flipping Coins
- 4.6.10 Practice with Bounds
- 4.6.11 Implications of Expectation
4.7 Sampling & Confidence
- 4.7.1 Law Of Large Numbers: Video
- 4.7.2 Not So Strong
- 4.7.3 Independent Sampling Theorem: Video
- 4.7.4 Sampling Coin Tosses
- 4.7.5 Birthday Matching: Video
- 4.7.6 Birthdays On Naboo
- 4.7.7 Sampling & Confidence: Video
- 4.7.8 Confidence
- 4.7.9 Random Sampling
- 4.7.10 Above Average Number of Fingers
4.8 Random Walks & Pagerank