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

Combinatorial Methods
Counting Rules, Combinatorial Techniques for Evaluating Probabilities. Examples

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

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 
L21 Multifactor Analysis of Variance
Extension of the Single-Factor Model, Significance Testing
Applications on MATLAB®
PS8 Due
PS9 Issued
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


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