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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