LEC/REC #  TOPICS  KEY DATES 

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 
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 
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 