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Computing and Data Analysis for Environmental Applications >> Content Detail



Study Materials



Readings

The readings listed below are from two textbooks:

D: Devore, Jay L. Probability and Statistics for Scientists and Engineers. Duxbury Press, 2000.
E: Etter, D. Introduction to MATLAB® for Engineers and Scientists. Prentice-Hall, 1996.

LEC # / REC #TOPICSREADINGS
L1Course Introduction
Course Logistics
Repeated Trials, Virtual Experiments, Probability, Statistics
D1.1
R1Programming in MATLAB®
Downloading Data, Accessing MATLAB®, MATLAB® Environment, Variables, Arrays, Scripts
Plotting Data
E2.1-2.6
L2Descriptive Statistics
Histograms, Percentiles, Mean, Median, Variance, etc.
Characterizing Streamflow Data
L3Probability
Experiments, Outcomes, Sample Spaces, Events, Probability, Axioms of Probability
Methods for Assigning Probabilities
D1.2-1.4
R2MATLAB® Operations
Internal MATLAB® Functions. Common MATLAB® Operations, Element-wise Computations, Loops
Translating Equations to Programs
E3.1-3.4
L4Joint Probability, Independence, Repeated Trials
Joint Probability, Independent Events, Repeated Trials
D2.1-2.2
L5

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

D2.3
R3MATLAB® Tests and Loops
Relational and Logical Operations, User-defined Functions, if Tests. Virtual Experiments
E3.5-3.6
L6Conditional Probability and Bayes Theorem
Joint Probability, Conditional Probability, Prior & Posterior Probabilities, Bayes Theorem
Engineering Applications
D2.4-2.5
L7Random Variables and Probability Distributions
Definition of a Random Variable
Cumulative Distribution Functions, Mass and Density Functions
Using Distributions to Assign Probabilities
R4Virtual Experiments
L8Expectation, 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
L9Risk
Defining and Evaluating Risk
Engineering Applications
D3.3
R5Quiz Review
Quiz 1
L10Some 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
L11Multivariate Probability
Multiple Random Variables, Joint and Conditional Distributions, Independence, Covariance and Correlation
Computing Conditional Probabilities in MATLAB®
D5.1-5.2
L12Functions of Many Random Variables 
Derived distributions for multivariate problems, moments of linear
functions of several random variables. Central Limit Theorem


R6Time Series and Central Limit Theorem
L13Populations and Samples 
Populations, random samples. Sample statistics, moments of the sample mean and variance.

D5.3-5.5
L14Estimation
Estimating Distributional Properties, Assessing Estimation Error
Comparing Alternative Estimators
D6.1-6.2
L15Confidence Intervals
Basic Concepts, Large Sample Confidence Intervals for the Population Mean
Computing Large Sample Confidence Intervals
D7.1-7.3
R7Review
L16Testing 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
L17Testing Hypotheses about Two Populations
Large Sample Tests of Hypotheses about Two Populations
Controlled Experiments
Applications Using MATLAB®
D9.1-9.3
R8Quiz Review
Quiz 2
L18

Small Samples
t, chi-squared and F statistics. Small sample confidence intervals and hypothesis tests. Applications using MATLAB®.


L19-L20Analysis of Variance (ANOVA)
Testing the Significance of a Single Factor, the F Test
Review of Quiz 2, ANOVA examples 
L21Multifactor Analysis of Variance
Extension of the Single-Factor Model, Significance Testing
Applications on MATLAB®
D11.1-11.4
Examples
L22Linear Regression
Objectives and Assumptions of Linear Regression, Estimating Regression Coefficients, Normal Equations
Some Typical Environmental Applications
D12.1-12.2
R11Quiz Review
L23Analyzing Regression Results
Accuracy of Regression Estimates and Predictions, Prediction Confidence Intervals, Testing Significance
Continuation of Environmental Examples
D12.3-12.4
Quiz 3
Some Practical Applications


 

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