Following are 125 pages of course lecture notes written for the [CVE303] Probability and Statistics for Engineers course which I taught at METU Cyprus in the 2018-19 Spring and 2019-20 Fall semesters. These notes follow the general outline of chapters 2-10 and 12 of Devore's Probability and Statistics for Engineering and the Sciences textbook. Beginning with the chapter on joint probability, the notes begin to diverge more and more from Devore's book; though they still borrow the chapter and section numbers and titles. The ANOVA section uses completely different notation from Devore, and the Regression section also organizes work differently. The notes further include various introductory, explanatory, and connective text which is (sorely) lacking in Devore.
Because students were engineers, I avoided proofs and large scale computations. This is the only probability or statistics course which these students will take, so it necessarily covers a wide range of material (only superficially). Throughout, I attempted to ground understanding with examples from discrete random variables where simple computations can be easily done by hand. The primary goal of the course was to reach confidence intervals for regression lines.
- Notes: Sample Spaces and Events.
- Notes: Axioms and Properties of Probabilty.
- Notes: Counting.
- Notes: Conditional Probability.
- Notes: Independence.
- Notes: Random Variables.
- Notes: Probability Mass Functions.
- Notes: Expected Values.
- Notes: Binomial Distribution.
- Notes: Hypergeometric and Negative Binomial.
- Examples: Computational Examples Using R.
- Summary: Distributions So Far (A Family Comparison).
- <Notes: Poisson.>
- Handout: Discrete Distributions in R.
- Notes: Probability Density and Distribution Functions.
- Notes: Normal, Exponential, Gamma, Chi-Squared (draft).
- Examples: Normal Distribution in R.
- More Examples: Normal Distribution in R (Critical Values).
- Review of Continuous Distributions.
- Notes: Joint Random Variables.
- Notes: Expected Values, Covariance, Correlation.
- Notes: Statistics from Joint RV.
- Notes: Distribution of Sample Means.
- Notes: Distribution of Linear Combinations.
- Notes: From Parameter Estimation to Confidence Interval and Hypothesis Testing.
- <Notes: Toy Discrete Examples.>
- Notes: Introduction to Confidence Intervals (CI).
- Notes: CI for Mean Using Normal (z) Distribution .
- Notes: CI for Mean Using t Distribution.
- Notes: CI for Variance Using χ2 Distribution.
- Notes: Introduction.
- Notes: Hypothesis Test Procedure.
(z- and t-Tests for Mean and Proportion) - Notes: Hypothesis Test Design.
(α, β, Power)
- Notes: Introduction.
- Notes: z-Tests for μX - μY .
- Notes: t-Tests for μX - μY .
("Two Sample" and "Pooled Variance") - Extra: Comparison of t-Tests.
- Notes: F-Tests for σX = σY.
- Notes: Paired Data and Blocking.
- Notes: Introduction.
- Notes: Analysis of Variance.
- Summary: ANOVA Tables.
- Notes: Honestly Significant Differences.
- Notes: Regression Model and Estimating β0, β1.
- Notes: Confidence Intervals for β0, β1 and Regression Line.
- Notes: Regression Tables.
- 2018-19 Spring Semester
- 2019-20 Fall Semester