Understand probability fundamentals

Apply mathematical foundations of uncertainty—sample spaces, events, Bayes' theorem, independence, distributions

Building rigorous statistical reasoning from first principles when intuitive probability reasoning fails

• · event space definition
• · probability assignments or mass functions

• · computed probabilities
• · conditional probabilities
• · Bayes' theorem applications

• · numpy
• · scipy.stats

Event space finite or countable; probabilities sum to 1; independence properly justified

Conditional probability undefined if P(A)=0; independence assumption violated causes wrong inference

• · Covers axioms, Bayes' theorem, independence, random variables
• · Foundation for both Bayesian and frequentist inference