1 Discrete Probability Distributions
1.1 Simulation of Discrete Probabilities
1.2 Discrete Probability Distributions
2 Continuous Probability Densities
2.1 Simulation of Continuous Probabilities
2.2 Continuous Density Functions
3 Combinatorics
3.1 Permutations
3.2 Combinations
3.3 Card Shuffling
4 Conditional Probability
4.1 Discrete Conditional Probability
4.2 Continuous Conditional Probability
4.3 Paradoxes
5 Distributions and Densities
5.1 Important Distributions
5.2 Important Densities
6 Expected Value and Variance
6.1 Expected Value
6.2 Variance of Discrete Random Variables
6.3 Continuous Random Variables
7 Sums of Random Variables
7.1 Sums of Discrete Random Variables
7.2 Sums of Continuous Random Variables
8 Law of Large Numbers
8.1 Discrete Random Variables
8.2 Continuous Random Variables
9 Central Limit Theorem
9.1 Bernoulli Trials
9.2 Discrete Independent Trials
9.3 Continuous Independent Trials
10 Generating Functions
10.1 Discrete Distributions
10.2 Branching Processes
10.3 Continuous Densities
11 Markov Chains
11.1 Introduction
11.2 Absorbing Markov Chains
11.3 Ergodic Markov Chains
11.4 Fundamental Limit Theorem
11.5 Mean First Passage Time
12 Random Walks
12.1 Random Walks in Euclidean Space
12.2 Gambler's Ruin
12.3 Arc Sine Laws
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