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Step By Step Probability - Table of Contents
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Overview
Preface
Table of Contents
About Author(s)
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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