probability formulas

Note: For independent events, the joint probability is the product of the marginal probabilities C Bayes' theorem is used to find conditional probability P(AIB) P(  

Total Probability Formula P(A) = P(AH1)P(H1) + ··· + P(AHn)P(Hn) The probability of A is the weighted average of the conditional probabilities P(AHi) with weights P(Hi)

Some basic probability rules 1 Kolmogorov axioms: (1) Total probability 1: P(S)= 1 (2) Nonnegativity: P(A) ≥ 0 (3) Addition formula: If A1,A2, are disjoint, then 

Basic Formulas in Probability Theory and Useful Identities Yevgeny Levanzov ∗ Useful identities and notions 1 ∀p ∈ R, (1 + p) ≤ ep Mostly used in the 

Probability Definitions and Rules Definitions: Experiment Formula: The probability of an event E with sample space S is given by: P(E) = n(E) n(S) = Success

PROBABILITY AND STATISTICS FORMULA SHEET The probability distribution of a discrete random variable Χ is described by the probability mass function 

This formula holds for all probability spaces Page 6 The Multiplication Rule Multiplying both sides of that formula by P(A)

6 sept 2011 · Formulas for probability theory SF2940 (23 pages) Example 1 1 If X has the probability density fX (x), Y = AX + b, and A is invertible, then Y 

CONDITIONAL PROBABILITY Discrete random variables EXAMPLE 4 EX: The following formulas define the behavior of conditional probabilities: P(A B) =

Combinatorial Probabilities Key concepts • Permutation: arrangement in some order • Ordered versus unordered samples: In ordered samples, the order of the