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Essentials of Mathematical Probability and Statistics
A First Course For the Mathematically Inclined
John Travis
Contents
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Contents
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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
Section
11.4
Hypothesis Test for the difference of two means
\(H_0 : \mu_1 = \mu_2\) vs \(H_a : \mu_1 \neq \mu_2\)