Homework Help is Here – Start Your Trial Now!
Math
Probability
2. Properties of the Conditional Probability Theorem: Let (N, »' , P) be a probability space. If Be where P(B)>0, then the function P( |B) is a probability function with domain= Proof: Exercise. According to the theorem, P( |B) is a probábility function with domain= s. Thus, it should satisfy the following properties: P(Ø|B) = o.

2. Properties of the Conditional Probability Theorem: Let (N, »' , P) be a probability space. If Be where P(B)>0, then the function P( |B) is a probability function with domain= Proof: Exercise. According to the theorem, P( |B) is a probábility function with domain= s. Thus, it should satisfy the following properties: P(Ø|B) = o.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question

Proof the ff. answer the first one only.

2. Properties of the Conditional Probability Theorem: Let (n, . P) be a probability space. If Ber where P(B)>0, then the function PC |B) is a probability function with domain= Proof: Exercise. According to the theorem, P( |B) is a probábility function with domain=st. Thus, it should satisfy the following properties: P(Ø|B) = 0. If A1,A2....An are mutually exclusive, events then Finite additivity: P(A,UAU...UAJB) = P(A;|B) +P(Az]B) + ... + P(AB). If A is an event then P(A°]B) = 1- P(A|B). If A, and Az are events then P(A,- Az|B) = P(A,|B) - P(A,A2|B). If A, and Az are events then P(A,UAz|B) = P(A,|B) + P(A2|B)- P(A,A2B). If A, and Az are events and A,CAz then P(A,|B) <P(A2|B). If A,, A2,....An are events then P(A,UA;U...UA,]B) < P(A,|B) +P(A2]B) + + P(A|B). ... O O o 0
Transcribed Image Text:2. Properties of the Conditional Probability Theorem: Let (n, . P) be a probability space. If Ber where P(B)>0, then the function PC |B) is a probability function with domain= Proof: Exercise. According to the theorem, P( |B) is a probábility function with domain=st. Thus, it should satisfy the following properties: P(Ø|B) = 0. If A1,A2....An are mutually exclusive, events then Finite additivity: P(A,UAU...UAJB) = P(A;|B) +P(Az]B) + ... + P(AB). If A is an event then P(A°]B) = 1- P(A|B). If A, and Az are events then P(A,- Az|B) = P(A,|B) - P(A,A2|B). If A, and Az are events then P(A,UAz|B) = P(A,|B) + P(A2|B)- P(A,A2B). If A, and Az are events and A,CAz then P(A,|B) <P(A2|B). If A,, A2,....An are events then P(A,UA;U...UA,]B) < P(A,|B) +P(A2]B) + + P(A|B). ... O O o 0
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer