Class Information

Syllabus

Wk Date  Topic   Remarks 1.1 13 Jan Basics: random variable, probability density distributions, cumulative distributions; event space & trials; Fundamental Thm of Calculus Fundamental Thm of Calculus   1.2 15 Probability v statistics; continuous v discrete random variables; Bernoulli trials & coin flips     2.1 20 Binomial distribution & repeated events; joint distribution; independent and dependent events E(Joint Dist) notes (2 dice)  2.2 22 Common distribution: uniform, binomial, exponential, normal/gaussian; Pascal's triangle and binomial coefficients     3.1 27 Counting principles and methods; probability calculation using event space numeration; combinatorics and probability Feller v1 ch 2 3.2 29 Binomial coefficient calculations/identities Feller v1 ch 2 4.1 3 Feb Monty Hall Paradox; linear regression Monty Hall refs 4.2 5 Principle Component Analysis (PCA)     5.1 10 Mean and Expectation in probability and statistics; Law of Large Numbers; (binomial dist) Hmwk1: Combinatorics 5.2 12 Variance in probability and statistics; Var(binomial dist) Helpful Notes for Hmwk 1  6.1 17 Quiz on Basic Definintions; Go over Quiz 6.2 19 Go over Quiz Problems   7.1 24 Quiz on Basic Definintions; Conditional probability   7.2 26 Risk Analysis and Expected Value Risk Analysis notes 8.1  3 Mar Convolution: Joint Distributions, Filters, Data Smoothing Convolution notes 8.2 5 Transformations, Eigenvalues, Eigenvectors; Revisit PCA Postponed 9.1 10 Demos and discussions of examples of convolutions Conditional probability refs 9.2 12 Finish Probability; Normal Distribution     10.1 24 Convolutions, for discrete and continuous Hmwk2 due Wed, 25 Mar 10.2 26 Quiz on Basic Definintions Hmwk3 due 11.1 31 Statististical Testing; Level of Confidence     11.2  2 Apr Project Topic Presentatons     12.1 7 Examples: Statistical Analysis      12.2 9 Examples: Statistical Analysis      13.1 14 General Methodology: Statistical Analysis     13.2 16 Hypothesis Testing     14.1 21 Sampling Theory     14.2 23 Project Presentations     15.1 28 Project Presentations

Textbook pages 1-15       pages 15-21       pages 23-68

Feller Vol 1, Ch 2, pages 52-64, Combinatorics Problems

Selected Basic Definitions:

Probability distribution functions

Convolutions

Conditional Probability:

Clearly Presented Conditional Probability Examples

Simple Conditional Probability Example w Applet

The Monty Hall Problem:

Let's Make a Deal Website (Monty Hall Problem): Background and Applet

Let's Make a Deal (Monty Hall) Applet

Nice Monty Hall Problem Demo Applet

Monty Hall Problem Data Simulator Applet

Monty Hall Problem discussed and analyzed (from the curious incident of the dog in the night-time by mark haddon)

And Behind Door No. 1, a Fatal Flaw (NYT 8 Apr 2008)

 

Expectation of Joint Distribution: 2 Dice:

Expectation for Sum of 2 Dice (rfr)

Notes on Joint Distributions and Convolution (rfr)

 

Binomial Distribution

Derivation Recursive Relationship for Binomial Coefficients

Derivation of E(X) and Var(X) for Binomial Distribution

 

Risk Analysis

Risk Analysis and Expected Value

 

Convolutions

Convolutions: Discrete and Continuous

 

Normal Distribution Illustrations:

Ball Drop

Flexible Normal Curve Shapes and Histogram Relationship

Interactive Normal Curve Shapes (go to bottom of target page)

Interactive Cumulative Area (Probability) Intervals

 

Linear Regression Analysis

Linear Regression (Yale Notes)

Linear Regression (Wikipedia)

Assumptions of Linear Regression

Linear Regression and Excel (Clemson Notes)

 

Statistical Analysis

Investigation Strategy.pdf

Investigation Strategy.doc

Resources