ENG EC 381 Lecture Notes - Lecture 2: Mutual Exclusivity, Probability Axioms, Countable Set

• School: Boston University
• Department: Electrical & Computer Engineering
• Course: ENG EC 381
• Professor: Vaishali Goyal

Document Summary

Lecture 2: probability axioms, p[a] 0, p[s] = 1, for any countably infinite collection of mutually exclusive events. A1, a2, , the probability law satisfies: p [ a1 u a2 u a3] = p[a1] + p[a2] + p[a3: for any disjoint events a1 & a2 : p[a1 u a2 ] = p[a1] +p[a2] P[ac] = 1 p[a: let a and b be events (assuming that they are not disjoint) P [a u b] - p [b] = p[a] +p[c] - p [c] - p [d] P [a u b] = p[a] +p[b] - p [d: conditional probability, the conditional probability of the event a given that the probability that event b (where p [b] > 0, p[a|b] = (p [ a n b])/(p[b]) Roll a six face d die: p[{4} | {outc o m e is eve n } ] = p[{4} n {2, 4, 6}]/ p[{2, 4, 6}] =