Abstract
To help teaching of machine learning course, manipulation rules and application examples of conditional probabilities in machine learning are presented. The emphasis is to make a clear distinction between reasonable assumptions and logical deductions developed from assumptions and axioms. The formula for conditional probability of conditional probability is presented with examples in Bayesian coin tossing, Bayesian linear regression, and Gaussian processes for regression and classification. The signal + noise model is formulated in terms of a proposition and exemplified by linear-Gaussian models and linear dynamical systems.
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