| LEC/REC # | TOPICS | KEY DATES |
|---|---|---|
| L1 |
Course Introduction Course Logistics Repeated Trials, Virtual Experiments, Probability, Statistics |
|
| R1 |
Programming in MATLAB® Downloading Data, Accessing MATLAB®, MATLAB® Environment, Variables, Arrays, Scripts Plotting Data |
|
| L2 |
Descriptive Statistics Histograms, Percentiles, Mean, Median, Variance, etc. Characterizing Streamflow Data |
|
| L3 |
Probability Experiments, Outcomes, Sample Spaces, Events, Probability, Axioms of Probability Methods for Assigning Probabilities |
PS1 Issued |
| R2 |
MATLAB® Operations Internal MATLAB® Functions. Common MATLAB® Operations, Element-wise Computations, Loops Translating Equations to Programs |
|
| L4 |
Joint Probability, Independence, Repeated Trials Joint Probability, Independent Events, Repeated Trials |
|
| L5 |
Combinatorial Methods |
PS1 Due PS2 Issued |
| R3 |
MATLAB® Tests and Loops Relational and Logical Operations, User-defined Functions, if Tests. Virtual Experiments |
|
| L6 |
Conditional Probability and Bayes Theorem Joint Probability, Conditional Probability, Prior & Posterior Probabilities, Bayes Theorem Engineering Applications |
|
| L7 |
Random Variables and Probability Distributions Definition of a Random Variable Cumulative Distribution Functions, Mass and Density Functions Using Distributions to Assign Probabilities |
PS2 Due PS3 Issued |
| R4 | Virtual Experiments | |
| L8 |
Expectation, Functions of a Random Variable Expectation, Population Mean and Variance Defining and Functions of a Single Random Variable Solving Derived Distribution Problems with Stochastic Simulation |
|
| L9 |
Risk Defining and Evaluating Risk Engineering Applications |
PS3 Due |
| R5 | Recitation 5 — Quiz Review | |
| Quiz 1 | ||
| L10 |
Some Common Probability Distributions Uniform, Exponential, Normal, and Lognormal Distributions Special Properties of Normal Random Variables Fitting Distributions to Data |
PS4 Issued |
| L11 |
Multivariate Probability Multiple Random Variables, Joint and Conditional Distributions, Independence, Covariance and Correlation Computing Conditional Probabilities in MATLAB® |
|
| L12 |
Functions of Many Random Variables Derived distributions for multivariate problems, moments of linear functions of several random variables. Central Limit Theorem |
|
| R6 | Time Series and Central Limit Theorem | |
| L13 |
Populations and Samples Populations, random samples. Sample statistics, moments of the sample mean and variance. |
PS4 Due PS5 Issued |
| L14 |
Estimation Estimating Distributional Properties, Assessing Estimation Error Comparing Alternative Estimators |
|
| L15 |
Confidence Intervals Basic Concepts, Large Sample Confidence Intervals for the Population Mean Computing Large Sample Confidence Intervals |
PS5 Due PS6 Issued |
| R7 | Review | |
| L16 |
Testing Hypotheses about a Single Population Formulating Hypothesis Testing Problems, Definitions Large Sample Tests of Hypotheses about a Single Population Applications Using MATLAB® |
|
| L17 |
Testing Hypotheses about Two Populations Large Sample Tests of Hypotheses about Two Populations Controlled Experiments Applications Using MATLAB® |
PS6 Due |
| R8 | Quiz Review | |
| Quiz 2 | ||
| L18 |
Small Samples |
PS7 Issued |
| L19-L20 |
Analysis of Variance (ANOVA) Testing the Significance of a Single Factor, the F Test |
PS7 Due PS8 Issued |
| Review of Quiz 2, ANOVA examples | ||
| L21 |
Multifactor Analysis of Variance Extension of the Single-Factor Model, Significance Testing Applications on MATLAB® |
PS8 Due PS9 Issued |
| Examples | ||
| L22 |
Linear Regression Objectives and Assumptions of Linear Regression, Estimating Regression Coefficients, Normal Equations Some Typical Environmental Applications |
|
| R11 | Quiz Review | |
| L23 |
Analyzing Regression Results Accuracy of Regression Estimates and Predictions, Prediction Confidence Intervals, Testing Significance Continuation of Environmental Examples |
PS9 Due |
| Quiz 3 | ||
| Some Practical Applications |