Part IX · Number Theory, Combinatorics and Algebra
55. Probability, Expectation and Random Processes
6 lessons•27 topics•Intermediate / Expert
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55.01Outline
Probability basics
- Events
- Union/intersection
- Independence
- Conditional probability
- Bayes theorem
55.02Outline
Random variables
- Discrete distributions
- Expectation
- Variance
- Covariance
- Linearity of expectation
55.03Outline
Common distributions
- Bernoulli
- Binomial
- Geometric
- Uniform
- Poisson introduction
55.04Outline
Algorithmic expectations
- Indicator variables
- Expected inversions
- Coupon collector
- Randomized quicksort expected complexity
55.05Outline
Probabilistic DP
- Expected steps to absorption
- Random walks
- Game expected value
- Markov chain modeling
55.06Outline
Randomized methods
- Reservoir sampling
- Random shuffling Fisher-Yates
- Random pivot
- Importance of unbiased sampling