Credits:
Semesters Offered
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