LEARNING OUTCOMES
- Analyze probabilities and expectations using tools such as conditioning, independence, linearity of expectations.
- Compute expectation and variance of common discrete and continuous random variables.
- Apply z-transforms and Laplace transforms to derive higher moments of random variables.
- Prove elementary theorems on probability.
- Analyze tail probabilities via Markov and Chebyshev inequalities.
- Generate random variables for simulation.
- Perform simulations of Poisson arrival processes as well as event-driven simulations.
- Compute sample estimators for mean and variance.
- Derive estimators for statistical inference, including MLE, MAP, and Bayesian estimators.
- Understand the application of probability to problems in machine learning, theoretical computer science, networking, cloud computing, and operations research.