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
L5 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  
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   
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  

Course Info

As Taught In
Fall 2003
Learning Resource Types
Problem Sets with Solutions
Exams with Solutions
Lecture Notes
Programming Assignments with Examples