Probability and Computing Course ID 15559 Description Probability theory is indispensable in computer science. It is at the core of artificial intelligence and machine learning, which require decision making under uncertainty. It is integral to computer science theory, where probabilistic analysis and ideas based on randomization form the basis of many important algorithms. It is a central part of performance modeling in computer networks and systems, where probability is used to predict delays, schedule resources, and provision capacity. This course gives an introduction to probability as it is used in computer science theory and practice, drawing on applications and current research developments as motivation and context. Key Topics Probability on events, discrete and continuous random variables, conditioning and Bayes, higher moments, Laplace transforms and z-transforms, Gaussians and central limit theorem, tails and stochastic dominance, heavy-tailed distributions, Poisson processes, simulation of random variables, estimators for mean and variance, maximum likelihood estimation (MLE). MAP estimation, Bayesian statistics, confidence intervals. Required Background Knowledge 15-259 does not assume any background in probability or statistics, and will satisfy the probability and statistics requirement for Computer Science and AI Majors in SCS. The course does assume knowledge of 3D calculus (e.g., single and double integrals, differentiation, Taylor-series expansions), discrete mathematics (e.g., sequences, combinatorics, asymptotic notation), and proof writing. Course Relevance This course 15-259 is for undergraduates. Graduate students should enroll in 15-559. Course Goals 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. Assessment Structure Homework: 15% In-Class Quizzes: 15% Two Midterms: 45% Final: 25% Course Link https://www.cs.cmu.edu/~fsaad/teaching/15259-F25/index.html
