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Essentials of Mathematical Probability and Statistics
John Travis
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Front Matter
Colophon
Author Biography
Preface
1
Statistical Measures
1.1
Making Inferences
1.2
Measurement Scales
1.3
Statistical Measures of Position
1.4
Statistical Measures of the Middle
1.5
Statistical Measures of Variation
1.6
Adjusting Statistical Measures for Grouped Data
1.7
Other Statistical Point Measures
1.8
Visual Statistical Measures - Graphical Representation of Data
1.9
Summary
1.10
Exercises
2
Regression
2.1
Creating Models
2.2
Best-fit Line
2.3
Correlation
2.4
Higher Degree Regression
2.5
Multi-variable Regression
3
Counting and Combinatorics
3.1
Counting without Counting?
3.2
General Counting Principles
3.3
Permutations
3.4
Combinations
3.5
Summary
3.6
Exercises
4
Probability Theory
4.1
Quantifying Uncertainty
4.2
Relative Frequency
4.3
Definition of Probability
4.4
Exercises
4.5
Conditional Probability
4.6
Bayes’ Theorem
4.7
Independence
4.8
Summary
4.9
More Exercises
5
Probability Functions
5.1
Probability Niches
5.2
Random Variables
5.3
Probability Functions
5.4
Expected Value
5.5
Generating Functions
5.6
Standard Units
5.7
Summary
5.8
Exercises
6
Distributions based upon Equally likely Outcomes
6.1
Selecting Randomly
6.2
Discrete Uniform Distribution
6.3
Continuous Uniform Distribution
6.4
Hypergeometric Distribution
6.5
Generating Functions for Uniform-based Distributions
6.6
Summary
6.7
Exercises
7
Distributions based upon Bernoulli Trials
7.1
Trials vs Successes
7.2
Binomial Distribution
7.3
Geometric Distribution
7.4
Negative Binomial
7.5
Generating Functions for Bernoulli-based Distributions
7.6
Summary
7.7
Exercises
8
Distributions based upon Poisson Processes
8.1
Time vs Changes
8.2
Poisson Distribution
8.3
Exponential Distribution
8.4
Gamma Distribution
8.5
Generating Functions for Poisson Process Distributions
8.6
Summary
8.7
Exercises
9
Normal Distributions
9.1
What is Bell-shaped?
9.2
The Normal Distribution
9.3
Chi-Square Distribution
9.4
Other "Bell Shaped" distributions
9.5
Generating Functions for Normal and Associated Distributions
9.6
Normal Distribution as a Limiting Distribution
9.7
Central Limit Theorem
9.8
Summary
9.9
Exercises
10
Estimation
10.1
How Close is Close?
10.2
Interval Estimates - Chebyshev
10.3
Point Estimates
10.4
Interval Estimates - Confidence Interval for p
10.5
Interval Estimates - Confidence Interval for
\(\mu\)
10.6
Interval Estimates - Confidence Interval for
\(\sigma^2\)
10.7
Exercises
11
Hypothesis Testing
11.1
Making a guess
11.2
Hypotheses and Errors
11.3
Hypothesis Test for one proportion
11.4
Hypothesis Test for one mean
11.5
Hypothesis Test for one variance
11.6
Summary
11.7
Exercises
12
Review of Calculus
12.1
Geometric Series
12.1.1
Geometric Series
12.1.2
Alternate Forms for the Geometric Series
12.2
Binomial SumsBinomial SeriesTrinomial Series
12.3
Negative Binomial Series
Back Matter
Index
Section
8.6
Summary
Here is a summary of the major points in this chapter:
TBA
