| L1 | Course Introduction
Course Logistics
Repeated Trials, Virtual Experiments, Probability, Statistics | D1.1 |
| R1 | Programming in MATLAB®
Downloading Data, Accessing MATLAB®, MATLAB® Environment, Variables, Arrays, Scripts
Plotting Data | E2.1-2.6
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| 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 | D1.2-1.4
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| R2 | MATLAB® Operations
Internal MATLAB® Functions. Common MATLAB® Operations, Element-wise Computations, Loops
Translating Equations to Programs | E3.1-3.4
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| L4 | Joint Probability, Independence, Repeated Trials
Joint Probability, Independent Events, Repeated Trials | D2.1-2.2
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| L5 | Combinatorial Methods
Counting Rules, Combinatorial Techniques for Evaluating Probabilities. Examples | D2.3
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| R3 | MATLAB® Tests and Loops
Relational and Logical Operations, User-defined Functions, if Tests. Virtual Experiments | E3.5-3.6
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| L6 | Conditional Probability and Bayes Theorem
Joint Probability, Conditional Probability, Prior & Posterior Probabilities, Bayes Theorem
Engineering Applications | D2.4-2.5
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| L7 | Random Variables and Probability Distributions
Definition of a Random Variable
Cumulative Distribution Functions, Mass and Density Functions
Using Distributions to Assign Probabilities | |
| 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 | D3.1-3.2,
E4.1-4.2
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| L9 | Risk
Defining and Evaluating Risk
Engineering Applications | D3.3 |
| R5 | 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 | D3.4-3.6,
D4.3-4.6
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| L11 | Multivariate Probability
Multiple Random Variables, Joint and Conditional Distributions, Independence, Covariance and Correlation
Computing Conditional Probabilities in MATLAB® | D5.1-5.2
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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 |
|
| R6 | Time Series and Central Limit Theorem | |
| L13 | Populations and Samples
Populations, random samples. Sample statistics, moments of the sample mean and variance. |
D5.3-5.5 |
| L14 | Estimation
Estimating Distributional Properties, Assessing Estimation Error
Comparing Alternative Estimators | D6.1-6.2 |
| L15 | Confidence Intervals
Basic Concepts, Large Sample Confidence Intervals for the Population Mean
Computing Large Sample Confidence Intervals | D7.1-7.3
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| 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® | D8.1-8.5 |
| L17 | Testing Hypotheses about Two Populations
Large Sample Tests of Hypotheses about Two Populations
Controlled Experiments
Applications Using MATLAB® | D9.1-9.3
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| R8 | Quiz Review | |
| Quiz 2 | |
| L18 | Small Samples
t, chi-squared and F statistics. Small sample confidence intervals and hypothesis tests. Applications using MATLAB®. |
|
| L19-L20 | Analysis of Variance (ANOVA)
Testing the Significance of a Single Factor, the F Test | |
| Review of Quiz 2, ANOVA examples | |
| L21 | Multifactor Analysis of Variance
Extension of the Single-Factor Model, Significance Testing
Applications on MATLAB® | D11.1-11.4 |
| Examples |
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| L22 | Linear Regression
Objectives and Assumptions of Linear Regression, Estimating Regression Coefficients, Normal Equations
Some Typical Environmental Applications | D12.1-12.2 |
| R11 | Quiz Review |
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| L23 | Analyzing Regression Results
Accuracy of Regression Estimates and Predictions, Prediction Confidence Intervals, Testing Significance
Continuation of Environmental Examples | D12.3-12.4 |
| Quiz 3 | |
| Some Practical Applications | |