概率论期中总结.docx

概率论期中总结
Chapter 1 Introduction to Probability
Experiments, Events and Sample Space
? Types共 6 页



Pr(A1?A2?A3) = Pr(A1) + Pr(A2) + Pr(A3) ? [Pr(A1A2) + Pr(A2A3) + Pr(A1A3)] + Pr(A1A2A3). ? For every n events A1, . . . , An,
nPr(?Ai)?i?1
n?Pr(A)??Pr(AA)??iiji?1i?ji?j?kPr(AiAjAk)??i?j?k?lPr(AiAjAkAl)?(?1)n?1Pr(AiAj...An)Chapter 2 Conditional Probability
The Definition of Conditional Probability
? Introduction to the Definition The conditional probability of the event A given that the event B has occurred.: Pr(A | B).
Pr(A|B)?Pr(AB)Pr(B)
Rewrite the formula of conditional probabilities: Pr(AB) = Pr(B)Pr(A | B). Pr(AB) = Pr(A)Pr(B | A). ? Intersection of n events Suppose that A1,A2, . . . ,An are events such that Pr(A1A2 · · ·An?1) > 0. Then
Pr(A1A2 · · ·An) = Pr(A1)Pr(A2 | A1)Pr(A3 | A1A2) … Pr(An| A1A2 · · ·An?1). Rewrite:
Suppose that A1,A2, . . . ,An,B are events such that Pr(A1A2 · · ·An?1 | B) > 0. Then
Pr(A1A2 · · ·An | B) = Pr(A1 | B)Pr(A2 | A1B) · · · Pr(An | A1A2 · · ·An?1B).
Independent Events
? Definition of Independence Suppose that Pr(A) > 0 and Pr(B) > 0. Events A and B are independent if Pr(A | B) = Pr(A), Pr(B | A) = Pr(B).










Theorem ? The