ENEE324: Engineering Probability

Credits: 3

Description

Axioms of probability; conditional probability and Bayes' rules; random variables, probability distribution and densities: functions of random variables: weak law of large numbers and central limit theorem. Introduction to random processes; correlation functions, spectral densities, and linear systems. Applications to noise in electrical systems, filtering of signals from noise, estimation, and digital communications.

Semesters Offered

Fall 2017, Spring 2018, Summer 2018, Fall 2018, Spring 2019, Summer 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021, Summer 2021, Fall 2021, Spring 2022, Summer 2022, Fall 2022, Spring 2023, Summer 2023, Fall 2023

Learning Objectives

• Understand the basic rules for manipulating probability densities in the computation of event probabilities, functions of random variables and expected values
• Understand pairs of random variables, random vectors and their marginal, joint and conditional probability distributions, conditional expectations
• Understand concepts of correlation and independence
• Understand sums of random variables, use of moment generating functions, central limit theorem
• Understand how means can be estimated using the sample mean; understand confidence intervals

Topics Covered

• Sample space and events
• Axioms of probability
• Computing probabilities
• Conditional probability and independence
• Sequential experiments
• Random variables
• Some important random variables
• Functions of a random variable and expected value
• Moment generating functions
• Multiple random variables
• Joint, marginal and conditional probability distributions
• Conditional expectation
• Covariance, correlation matrices
• Functions of multiple random variables
• Sums of independent random variables
• Central limit theorem
• Sample mean
• Introduction to parameter estimation via sample mean, confidence intervals