| 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
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| 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
Counting Rules, Combinatorial Techniques for Evaluating Probabilities. Examples | PS1 Due
PS2 Issued
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| 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
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| 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
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| L11 | Multivariate Probability
Multiple Random Variables, Joint and Conditional Distributions, Independence, Covariance and Correlation
Computing Conditional Probabilities in MATLAB® |
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| L12 | Functions of Many Random Variables
Derived distributions for multivariate problems, moments of linear
functions of several random variables. Central Limit Theorem |
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| 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
t, chi-squared and F statistics. Small sample confidence intervals and hypothesis tests. Applications using MATLAB®. |
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 |
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| 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 | |