Introduction to probability and its role in modeling and analyzing real world phenomena and systems, including topics in statistics, machine learning, and statistical signal processing. Elements of probability, conditional probability, Bayes rule, independence. Discrete and continuous random variables. Signal detection. Functions of random variables. Expectation; mean, variance and covariance, linear MSE estimation. Conditional expectation; iterated expectation, MSE estimation, quantization and clustering. Parameter estimation. Classification. Sample averages. Inequalities and limit theorems. Confidence intervals. Prerequisites: Calculus at the level of MATH 51, CME 100 or equivalent and basic knowledge of computing at the level of CS106A.