probability

## What I do - Calculate probabilities and conditional probabilities - Apply Bayes' theorem for inference - Work with probability distributions (discrete and continuous) - Calculate expected values and variances - Apply the central limit theorem - Use moment generating functions ## When to use me When analyzing random phenomena, making inferences from data, or modeling uncertainty. ## Key Concepts - **Probability Axioms**: P(A) ≥ 0, P(S) = 1, P(∪A_i) = ΣP(A_i) for disjoint events - **Conditional Probability**: P(A|B) = P(A∩B)/P(B) - **Bayes' Theorem**: P(A|B) = P(B|A)P(A)/P(B) - **Expected Value**: E[X] = Σ x·P(X=x) or ∫x·f(x)dx - **Variance**: Var(X) = E[X²] - (E[X])² - **Central Limit Theorem**: Sum of i.i.d. variables approaches normal distribution