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**By this book you will cover this topic:**

**Fundamentals of Probability **

- Theoretical Approaches
- A More Intuitive Approach
- Our Definitions
- Bus Ridership Model
- Aloha Network
- Aloha Network Model Summary
- Aloha Network Computations
- Aloha in the Notebook Context
- A Simple Board Game

**Functions **

- Discrete Random Variables
- Random Variables
- Discrete Random Variables
- The Monty Hall Problem
- Expected Value
- Misnomer
- Bus Ridership
- Predicting Product Demand
- Expected Values via Simulation

**The Gamma Family of Distributions **

Density and properties

Network Buffer

Importance in modeling

**The Beta Family of Distributions**

- Density etc
- Importance in Modeling

**Mathematical Complements **

- Hazard Functions
- Duality of the Exponential Family with the Poisson
- Family

**Computational Complements**

- R’s integrate() Function
- Inverse Method for Sampling from a Density
- Sampling from a Poisson Distribution

**Cumulative Distribution Functions **

- CDFs
- Non-Discrete, Non-Continuous Distributions

**Density Functions**

- Properties of Densities
- Intuitive Meaning of Densities
- Expected Values
- A First Example

** Famous Parametric Families of Continuous Distributions**

- The Uniform Distributions
- Density and Properties
- R Functions
- Modeling of Disk Performance
- Modeling of Denial-of-Service

**The Normal Family of Continuous Distributions**

- Importance in Modeling
- The Exponential Family of Distributions

**Density and Properties** - R Functions
- Garage Parking Fees
- Memoryless Property of Exponential Distributions
- Importance in Modeling