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Essentials of Mathematical Probability and StatisticsA First Course For the Mathematically Inclined

John Travis

Front Matter

Colophon
Author Biography
Preface

1 Statistical Measures

Introduction
Measurement Scales
Statistical Measures of Position
Statistical Measures of the Middle
Statistical Measures of Variation
Adjusting Statistical Measures for Grouped Data
Other Statistical Point Measures
Visual Statistical Measures - Graphical Representation of Data
Exercises

2 Regression

Introduction
Linear Regression - Best Fit Line
Correlation
Higher Degree Linear Regression
Multi-variable Linear Regression

3 Counting and Combinatorics

Introduction
General Counting Principles
Permutations
Combinations
Exercises

4 Probability Theory

Introduction
Relative Frequency
Definition of Probability
Exercises
Conditional Probability
Bayes Theorem
Independence
More Exercises

5 Probability Functions

Introduction
Random Variables
Probability Functions
Expected Value
Standard Units
Exercises - Probability Functions and Random Variables

6 Distributions based upon Equally likely Outcomes

Introduction
Discrete Uniform Distribution
Continuous Uniform Distribution
Hypergeometric Distribution
Exercises

7 Distributions based upon Bernoulli Trials

Introduction
Binomial Distribution
Geometric Distribution
Negative Binomial
Exercises

8 Distributions based upon Poisson Processes

Introduction
Poisson Distribution
Exponential Distribution
Gamma Distribution
Exercises

9 Normal Distributions

Introduction
The Normal Distribution
Chi-Square Distribution
Other "Bell Shaped" distributions
Normal Distribution as a Limiting Distribution
Central Limit Theorem
Exercises

10 Estimation

Introduction
Interval Estimates - Chebyshev
Point Estimates
Interval Estimates - Confidence Interval for p
Interval Estimates - Confidence Interval for $\mu$
Interval Estimates - Confidence Interval for $\sigma^2$
Exercises

11 Hypothesis Testing

Introduction
Hypothesis Test for one proportion
Hypothesis Test for one mean
Hypothesis Test for the difference of two means
Hypothesis Test for one variance

12 Review of Calculus

Geometric Series
Binomial SumsBinomial SeriesTrinomial Series
Negative Binomial Series

Authored in PreTeXt

Chapter 12 Review of Calculus

This chapter is a review of power series results from Calculus.

12.1 Geometric Series
12.2 Binomial SumsBinomial SeriesTrinomial Series
12.3 Negative Binomial Series