ffsshhttiikk 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