16.322 Stochastic Estimation and Control, Fall 2004 Prof vander velde Compound Events A+B+C,or"i means the event A occurs, or B occurs, or C occurs, or any combination of them occur ABC. and" means the event a and b and c occur A, not, means the event a does not occur; Complementary event A A+B+C Venn diagram Probability Functions The probability measure of an event is the integral of the probability function over the set of outcomes favorable to the event. One definition: P(E)=lim n(E) 月→∞ Properties of probability functions P(empty set)=0 P(sample space)=1 0≤P(E)<1 Basic axiom of probability: Probabilities for the sum of mutually exclusive events dd P(A+B+C)=P(A)+P(B)+P(C) Page 3 of 716.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Compound Events A+B+C, “or”; means the event A occurs, or B occurs, or C occurs, or any combination of them occur ABC, “and”; means the event A and B and C occur A , “not”; means the event A does not occur; Complementary event Venn diagram Probability Functions The probability measure of an event is the integral of the probability function over the set of outcomes favorable to the event. One definition: n E () = lim ( ) PE n→∞ N Properties of probability functions: P(empty set) = 0 P(sample space) = 1 0 ≤ P E( ) < 1 Basic axiom of probability: Probabilities for the sum of mutually exclusive events add. PA B C ( + + ) = PA ( ( ( ) + PB ) + PC ) Page 3 of 7