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, Elementwise 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

R3 
MATLAB® Tests and Loops
Relational and Logical Operations, Userdefined 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
t, chisquared and F statistics. Small sample confidence intervals and hypothesis tests. Applications using MATLAB®.

PS7 Issued 
L19L20 
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 SingleFactor 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 
