4 notes example 20 independence and law of total

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 7.4 Notes Example 20 Independence and Law of Total Probability Notes The independence of the events A and B implies that the following are independent: 1 Ac and B 2 A and B c 3 Ac and B c Independence Law of Total Probability 7.5 Example 20 Independence and Law of Total Probability Solution. Independence Law of Total Probability 7.6 Notes Independence for more than two events Independence and Law of Total Probability Notes Consider more than two events A1 , A2 , · · · , Ak , we have two types of independence: Pairwise independent P(Ai ∩ Aj ) = P(Ai ) × P(Aj ) i , j ∈ 1, 2, · · · , k i = j Independence Law of Total Probability Mutually independent P(Ak1 ∩ Ak2 ∩ · · · ∩ Akn ) = P(Ak1 ) × P(Ak2 ) × · · · × P(Akn ) ki , kj ∈ 1, 2, · · · , k ki = kj 1 ≤ n ≤ k 7.7 Example 21 Chris and his roommates each have a car. Julia’s Mercedes SLK works with probability .98, Alex’s Mercielago Diablo works with probability .91, and Chris’ 1987 GMC Jimmy works with probability .24. Ass...
View Full Document

This note was uploaded on 01/24/2014 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue University-West Lafayette.

Ask a homework question - tutors are online