# In order to have such independence a stronger

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: would not consider them to be physically independent. However, A = {2, 4, 6}, B = {3, 6}, and AB = {6}. So P (A) = 1 , 2 P (B ) = 1 and P (AB ) = 1 . Therefore, P (AB ) = P (A)P (B ), which means that A and B are 3 6 mutually independent. This is a simple example showing that events can be mutually independent, even if they are not physically independent. Here is a ﬁnal note about independence of two events. Suppose A is independent of B. Then P (Ac B ) = P (B ) − P (AB ) = (1 − P (A))P (B ) = P (Ac )P (B ), so Ac is independent of B. Similarly, A is independent of B c , and therefore, by the same reasoning, Ac is independent of B c . In summary, the following four conditions are equivalent: A is independent of B , Ac is independent of B , A is independent of B c , Ac is independent of B c . Let us now consider independence conditions for three events. The following deﬁnition simply requires any one of the events to be independent of any one of the other events. Deﬁnition 2.4.4 Events A, B, and C are pairwise independent...
View Full Document

## This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

Ask a homework question - tutors are online