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Essentials of Mathematical Probability and Statistics
John Travis
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Contents
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Front Matter
Colophon
Author Biography
Preface
1
Statistical Measures
Making Inferences
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
Summary
Exercises
2
Regression
Creating Models
Best-fit Line
Correlation
Higher Degree Regression
Multi-variable Regression
3
Counting and Combinatorics
Counting without Counting?
General Counting Principles
Permutations
Combinations
Summary
Exercises
4
Probability Theory
Quantifying Uncertainty
Relative Frequency
Definition of Probability
Exercises
Conditional Probability
Bayes' Theorem
Independence
Summary
More Exercises
5
Probability Functions
Probability Niches
Random Variables
Probability Functions
Expected Value
Generating Functions
Standard Units
Summary
Exercises
6
Distributions based upon Equally likely Outcomes
Selecting Randomly
Discrete Uniform Distribution
Continuous Uniform Distribution
Hypergeometric Distribution
Generating Functions for Uniform-based Distributions
Summary
Exercises
7
Distributions based upon Bernoulli Trials
Trials vs Successes
Binomial Distribution
Geometric Distribution
Negative Binomial
Generating Functions for Bernoulli-based Distributions
Summary
Exercises
8
Distributions based upon Poisson Processes
Time vs Changes
Poisson Distribution
Exponential Distribution
Gamma Distribution
Generating Functions for Poisson Process Distributions
Summary
Exercises
9
Normal Distributions
What is Bell-shaped?
The Normal Distribution
Chi-Square Distribution
Other "Bell Shaped" distributions
Generating Functions for Normal and Associated Distributions
Normal Distribution as a Limiting Distribution
Central Limit Theorem
Summary
Exercises
10
Estimation
How Close is Close?
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
Making a guess
Hypotheses and Errors
Hypothesis Test for one proportion
Hypothesis Test for one mean
Hypothesis Test for one variance
Summary
Exercises
12
Review of Calculus
Geometric Series
Binomial SumsBinomial SeriesTrinomial Series
Negative Binomial Series
Authored in PreTeXt
Section
9.8
Summary
Here is a summary of the major points in this chapter:
TBA