Lecture Notes for ECE302 section 3, Fall 2021

Content last revised: 12/10/2021 (Semester overview posted at bottom)

12/5/21: (Final revision of Random Processes Lecture Notes posted.)

Topic 1: Probability of Events

Topic 1.1: Set theory (reading Chapter 2.1.3)

Topic 1.2: Random Experiments (reading Chapter 1 and 2.1)

What is the sample space? (blank with no solutions)

Topic 1.3: Axioms and their corollaries (reading Chapter 2.2)

An interlude: Assigning probability models (reading Chapter 2.2.1 and 2.2.2)

Topic 1.4: Conditional probability (part 1) (reading Chapter 2.4)

Conditional probability (part 2)

Topic 1.5: Independence of events (reading Chapter 2.5)

Topic 1.6: Sequential experiments (reading Chapter 2.6.1 and 2.6.5)

Review of topic 1

Topic 2: One Random Variable

Topic 2.1: Intro to random variables, and the Probability Mass Function (PMF) (reading Chapter 3.1 and 3.2)

Topic 2.2 (part 1): Cumulative Distribution Function (CDF) (reading Chapter 4.1)

Topic 2.2 (part 2): Probability Density Function (PDF) (reading Chapter 4.2 (except not Chapter 4.2.2))

REVISED 9/24/21 Topic 2.3: Moments (e.g., expectations and variance) (reading Chapter 3.3 and 4.3)
(change was to last 2 equations at the bottom of page 13)

Topic 2.4 (part 1): Common PMFs (reading Chapter 3.5 and 2.6.2 and 2.6.4)

Introduction

Geometric

Binomial

Poisson

Topic 2.5 (part 1): Conditional PMF, CDF, PDF conditioned on an event (reading Chapter 3.4 and Chapter 4.2.2)

Topic 2.4 (part 2): Common PDFs (Gaussian/Normal, .) (reading Chapter 4.4)

Topic 2.5 (part 2): Conditional mean, conditional variance, theorem of total expectation (reading 3.4.2)

Topic 2.6: PDF of Y=g(X) (reading Chapter 4.5)

Topic 2.7: Hypothesis testing (added 10/22/21)

Review Topic 2

Topic 3: Two or more Random Variables

Preview Topic 3

Topic 3.1: Joint PMF, CDF, PDFs (reading Chapters 5.1-5.4)

Topic 3.2: Independence of RVs (reading chapter 5.5)

Topic 3.3: Joint moments (correlation, covariance, correlation coefficient) (reading chapter 5.6)

Topic 3.4a: Conditional PDF conditioned on a RV (definition only) (reading Chapter 5.7)

Topic 3.4b: Building models and inference using 2 RVs

Topic 3.4c: Conditional Expectation and Iterated Expectation

Topic 3.4d: Parameter estimation (will not explicitly be covered in Fall 2021)

More of Topic 3: (Two or more RVs)

Topic 3.7: Weak Law of Large Numbers (revised 11/17/21 at 11am)

Central Limit Theorem

Examples of LLN and CLT

Topic 3.8: Functions of 2 random variables

NEWER VERSIONS Topic 4: Random Processes

Topic 4.1: Intro to random processes (updated 11/29/21) << Examples of X(t) and X_n, and mean and variance functions

Topic 4.2: Autocorrelation, autocovariance, cross-correlation and cross-covariance (updated 11/30/21) << How are X(t_1) and Y(t_2) related?

Topic 4.3: Wide-sense stationary random processes (updated 11/30/21) << defining a useful subset of RPs based on their autocorrelation function

Topic 4.4: Power spectral density and linear time invariant system (updated 12/5/21) << Fourier transform of the autocorrelation function

Semester-end overview

Semester end overview fall 2021