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Step By Step Probability - Table of Contents

Offering: Step By Step Probability

Titles: Step By Step Probability I, Probability: Audible Lecture Series

By Dr. Michael Kouritzin

  • 1. Introduction
    • 1.0 - Introduction
  • 2. Counting and Probability
    • 2.1 - Equally Likely Conditional Probability
    • 2.2 - Permutations and Combinations
    • 2.3 - Multinomial and Hypergeometric Distributions
    • 2.4 - Maximum Likelihood Estimation
    • 2.5 - Sample Space and Events
    • 2.6 - Probability and Conditional Probability
    • 2.7 - Total Probability and Bayes' Rule
    • 2.8 - Independence
    • 2.9 - Texas Hold'em*
  • 3. Theory of Random Vectors
    • 3.1 - Discrete Vectors and the pmf
    • 3.2 - Distribution and Reliability
    • 3.3 - Expectation, Covariance and Correlation
    • 3.4 - Moments and Moment Generating Function
    • 3.5 - Independence of Random Vectors
    • 3.6 - Strong Law of Large Numbers
    • 3.7 - Conditional Expectation
    • 3.8 - Conditional Expectation Estimators
    • 3.9 - Practical Applications of Conditional Expectation
    • 3.10 - Innovation representation
  • 4. Probability of Independent Trials
    • 4.1 - Probability of Independent Trials
    • 4.2 - Geometric and Negative Binomial elements
    • 4.3 - Simple Random Walks
    • 4.4 - Gambler's Ruin
    • 4.5 - Transience and Recurrence
    • 4.6 - Insurance Claims*
  • 5. Continuous Random Vectors
    • 5.1 - Continuous Random Vectors
    • 5.2 - Uniform Random Variables
    • 5.3 - Independence and Conditional Expectation
    • 5.4 - Exponential Distributions
    • 5.5 - Simulating Continuous Random Variables
    • 5.6 - Moment Generating Functions
  • 6. Reliability and Continuous Random Vectors
    • 6.0 - Life Expectancy
    • 6.1 - Combining Continuous Random Variables
    • 6.2 - Gamma Random Variables
    • 6.3 - Weibull Distributions
    • 6.4 - Reliability and Hazard Rate*
  • 7. Statistical Tests and Estimation
    • 7.1 - Linear Regression
    • 7.2 - The Normal Distribution
    • 7.3 - The Central Limit Theorem
    • 7.4 - Hypothesis Testing*
  • 8. List Length and Counting Processes
    • 8.0 - Hashing
    • 8.1 - Poisson Variables
    • 8.2 - Poisson Measures and Processes
    • 8.3 - Poisson Process Limit
    • 8.4 - Simulating the Poisson Process
    • 8.5 - Characterizing Poisson Process*
    • 8.6 - Task Stream Poisson Process*
  • 9. Data Communications and Queuing Processes
    • 9.0 - Internet and Communication Networks
    • 9.1 - Bernoulli Single Server Queues
    • 9.2 - M/M/1 Queue
    • 9.3 - M/M/k Queue and Markov Queuing
    • 9.4 - Steady State Probabilities in M/M/k and BSSQ
    • 9.5 - Customer Times and Little's Formula
  • 10. Notation and Formulae
    • 10.1 - Notation List
    • 10.2 - Formulae List
    • 10.3 - Probability Tables
  • 11. Calculus Problems
    • 11.1 - Limits, Derivatives, Series, Definite Integrals
    • 11.2 - Series, Partial Derivative, Integration
  • 12. Extras
    • 12.1 - Statistical Estimators
    • 12.2 - Regression*
    • 12.3 - Black-Scholes Model*
    • 12.4 - Unequal Servers*
    • 12.5 - More on Queuing Models*
    • 12.6 - More on Customer Time Proofs*
    • 12.7 - Biological Models
    • 12.8 - The Markov Property and Chains
    • 12.9 - Simple Markov Chains
    • 12.10 - Calculation in Simple Markov Chains
    • 12.11 - Markov Chain Simulation and Stationary Distributions
    • 12.12 - Recurrence and Transience of Markov Chains