ECE 3077 Summer 2014, Notes

Notes 0, Introduction and Background

I. Introduction to Probability
Notes 1, probability models
Notes 2, independence
Notes 3, conditional probability
Notes 4, Bayes rule
Notes 5, counting

II. Discrete Random Variables
Notes 6, discrete random variables, pmfs, examples
Notes 7, expectation
Notes 8, multiple (discrete) random variables, conditional pmfs, conditional expectation
Notes 9, independent random variables

III. Continuous Random Variables
Notes 10, pdfs, cdfs, expectation and variance
Notes 11, compendium of continuous random variables
Notes 12, joint pdfs
Notes 13, conditional pdfs, conditional expectation, iterated expectation
Notes 14, independent random variables
Notes 15, covariance
Notes 16, Bayes rule for random variables

IV. Functions of Random Variables
Notes 17, mapping random variables, sums of independent random variables
Notes 18, the central limit theorem

V. Introduction to Statistical Inference
Notes 19, the sample mean
Notes 20, confidence intervals