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Probability and Statistics - Home
  • Course Notes: Probability and Statistics

Probability

  • Basic Probability
    • Two Simple Tools
    • Probability Playground
    • Exercises
    • Solutions to Exercises
  • Counting Patterns
  • Compound Events
    • Independent Events
    • Odds
  • Partitions
  • Conditional Probability
    • Excercises
    • Solutions to Exercises
  • Binomial Theorem
    • Discrete Probability Functions
    • Worked Examples
    • Exercises
    • Solutions to Selected Exercises
  • Expected Value
    • Exercises
    • Solutions
  • Excercises
    • 50 Counting Questions
    • 50 Probability Questions
    • 85 More Probability Questions

Statistics

  • R and Basic Statistical Functions
    • Data Frames
    • Descriptive Statistics
    • Visualizing Data in R
  • Exploratory Data Analysis: Tools and Ideas
    • Exploratory Data Analysis
  • Sampling Distributions, the Central Limit Theorem and the Law of Large Numbers
    • The Central Limit Theorem and Estimation of the Mean
    • Sampling Distributions Examples
  • Normal Curve
    • Calculations with the Normal Curve
    • The \(z\)-Proportion Test
  • \(t\)-Tests
    • The \(t\)-Test
    • Independent Samples \(t\)-Test
    • Matched Pairs \(t\)-Test
    • Small Samples and \(t\)-Tests
  • Proportion Testing
    • The \(\chi^2\) Test of Independence
    • Goodness of Fit (GOF)
  • ANOVA
  • Correlation and Regression
  • Statistical Estimation

Appendix

  • Overview, Index, Links
  • Statistical Formulas
  • Helpful Code
    • Graphics Options
    • Creating a Data Frame
    • Creating a Data Frame
    • Grid of Graphics
    • Outliers
  • Statistics Formula Sheet
  • Sampling Functions
  • Poker Primer
  • Binder
  • .ipynb

Overview, Index, Links

Contents

  • Index of Appendix Pages

Overview, Index, Links#

We utilize the open source freeware R in this course. These appendices help clarify and store several important tasks for quick reference.

The most important appendix is the Statistical Formula Sheet which is allowed for use on tests and quizzes for this course and is provided for tests in the in-person version of the course.

When using R, several tasks are used quite often without a detailed explanation given for each use. We therefore have created a reference page for the most common uses. We have several pages in this section that deal with typical issues and the code in R that gets around them.

Index of Appendix Pages#

The following list describes the contents of each page:

  1. Statistical Formulas: Key notation for understanding R commands and statistical models.

  2. Helpful Code: Basic tasks in R like calculating standard descriptives and the 5-Number Summary along with using the cat() function to display text and code output together.

  3. Graphics Options: How to set main titles, axis titles along with changes of color and line width.

  4. Subsetting a Data Frame: Using the subset() function to extract specific types of data points from a data frame.

  5. Creating a Data Frame: Entering data into R by creatinng vectors using the concatenate function c() and then joining them into a dataframe.

  6. Creating a Grid of Graphics: When displaying multiple graphical objects at once, we can use the layout() and matrix() functions to create a grid. The graphical objects will be reduced in size and laid out as we specify. The result saves space and helps to organize content in a more meaningful way.

  7. Sampling Functions:

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Statistical Estimation

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Statistical Formulas

Contents
  • Index of Appendix Pages

By Robb Sinn

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