Chapters

  • 1 Before We Start ... Some Mathematical Basics
  • 2 Probability on Events
  • 3 Common Discrete Random Variables
  • 4 Expectation
  • 5 Variance, Higher Moments, and Random Sums
  • 6 z-Transforms
  • 7 Continuous Random Variables: Single Distribution
  • 8 Continuous Random Variables: Joint Distributions
  • 9 Normal Distribution
  • 10 Heavy Tails: The Distributions of Computing
  • 11 Laplace Transforms
  • 12 The Poisson Process
  • 13 Generating Random Variables for Simulation
  • 15 Estimators for Mean and Variance
  • 16 Classical Statistical Inference
  • 17 Bayesian Statistical Inference
  • 18 Tail Bounds
  • 19 Applications of Tail Bounds: Confidence Intervals and Balls and Bins
  • 20 Hashing Algorithms
  • 21 Las Vegas Randomized Algorithms
  • 22 Monte Carlo Randomized Algorithms
  • 23 Primality Testing
  • 24 Discrete-Time Markov Chains: Finite-State
  • 25 Ergodicity for Finite-State Discrete-Time Markov Chains
  • 26 Discrete-Time Markov Chains: Infinite-State
  • 27 A Little Bit of Queueing Theory