The catalog description for Foundations of Probability and Statistics-Calculus (MATH 2050) Based is: "Provides a calculus-based introduction to probability and statistical inference. Basic probability concepts, mathematical expectation, discrete and continuous probability distributions, sampling distributions, one and two-sample estimation, and hypothesis testing techniques are developed and used; includes linear regression and correlation."
The prerequisite is Calculus 1 (MATH 1910).
Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer and they contain proofs of the results from the class notes. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors).
Chapter 1. Sampling and Descriptive Statistics.
Chapter 2. Probability.
- Introduction. Chapter 2 Introduction notes
- Section 2.1. Basic Ideas. Section 2.1 notes
- Section 2.2. Counting Methods. Section 2.2 notes
- Section 2.3. Conditional Probability and Independence.
- Section 2.4. Random Variables.
- Section 2.5. Linear Functions of Random Variables.
- Section 2.6. Jointly Distributed Random Variables.
Chapter 3. Propogation of Error.
- Introduction.
- Section 3.1. Measurement Error.
- Section 3.2. Linear Combinations of Measurements.
- Section 3.3. Uncertainties for Functions of One Measurement.
- Section 3.4. Uncertainties for Functions of Several Measurements.
Chapter 4. Commonly Used Distributions.
- Introduction.
- Section 4.1. The Bernoulli Distribution.
- Section 4.2. The Binomial Distribution.
- Section 4.3. The Poisson Distribution.
- Section 4.4. Some Other Discrete Distributions.
- Section 4.5. The Normal Distribution.
- Section 4.6. The Lognormal Distribution.
- Section 4.7. The Exponential Distribution.
- Section 4.8. Some Other Continuous Distributions.
- Section 4.9. Some Principles of Point Estimation.
- Section 4.10. Probability Plots.
- Section 4.11. The Central Limit Theorem.
- Section 4.12. Simulation.
Chapter 5. Confidence Intervals.
- Introduction.
- Section 5.1. Large-Sample Confidence Intervals for a Population Mean.
- Section 5.2. Confidence Intervals for Proportions.
- Section 5.3. Small-Sample Confidence Intervals for a Population Mean.
- Section 5.4. Confidence Intervals for the Difference Between Two Means.
- Section 5.5. Confidence Intervals for the Difference Between Two Proportions.
- Section 5.6. Small-Sample Confidence Intervals for the Difference Between Two Means.
- Section 5.7. Confidence Intervals with Paired Data.
- Section 5.8. Prediction Intervals and Tolerance Intervals.
- Section 5.9. Using Simulation to Construct Confidence Intervals.
Chapter 6. Hypothesis Testing.
- Introduction.
- Section 6.1. Large-Sample Tests for a Population Mean.
- Section 6.2. Drawing Conclusions from the Results of Hypothesis Tests.
- Section 6.3. Tests for a Population Proportion.
- Section 6.4. Small-Sample Tests for a Population Mean.
- Section 6.5. Large-Sample Tests for the Difference Between Two Means.
- Section 6.6. Tests for the Difference Between Two Proportions.
- Section 6.7. Small-Sample Tests for the Difference Between Two Means.
- Section 6.8. Tests with Paired Data.
- Section 6.9. Distribution-Free Tests.
- Section 6.10. The Chi-Square Test.
- Section 6.11. The F Test for Equality of Variance.
- Section 6.12. Fixed-Level Testing.
- Section 6.13. Power.
- Section 6.14. Multiple Tests.
- Section 6.15. Using Simulation to Perform Hypothesis Tests.
Chapter 7. Correlation and Simple Linear Regression.
- Introduction.
- Section 7.1. Correlation.
- Section 7.2. The Least-Squares Line.
- Section 7.3. Uncertainties in the Least-Squares Coefficients.
- Section 7.4. Checking Assumptions and Transforming Data.
Additional chapters:
- Chapter 3. Propogation of Error.
- Chapter 8. Multiple Regression.
- Chapter 9. Factorial Experiments.
- Chapter 10. Statistical Quality Control.
Return to
Bob Gardner's home page
