| 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 |
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| 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
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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 |
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| R4 |
Virtual Experiments |
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| 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 |
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Quiz 1 |
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| 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 |
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| R6 |
Time Series and Central Limit Theorem |
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| 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 |
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| 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 |
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Quiz 2 |
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| L18 |
Small Samples
t, chi-squared and F statistics. Small sample confidence intervals and hypothesis tests. Applications using MATLAB®.
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|
| L19-L20 |
Analysis of Variance (ANOVA)
Testing the Significance of a Single Factor, the F Test |
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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® |
D11.1-11.4 |
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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 |
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Quiz 3 |
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Some Practical Applications |
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