# ENG EC 381 Lecture Notes - Lecture 3: Pairwise Independence, Fair Coin, Conditional Independence

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## Document Summary

If event a and b are independent, this means that the p[a|b] = p[a]: mutual independence, events a1, a2, an are mutually independent if a. i. All collection of n-1 events chosen from a1, a2, an are mutually independent a. ii. Note: for n = 2, mu t u al inde p e n d e n c e is syno n y m o u s with inde p e n d e n c e. Any collectio n of mutually independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent. a. iii. N= 3 a1, a2, a3 are mutually independent when. P[a1 n a3] = p[a1]p[a3: ex1. Flip a fair coin twice (each possible outcome is equally likely) E1 = {1st flip is h} = {hh, ht} E2 = {2nd flip is h} = {th, hh} E3 = {both flips are different} = {ht, th} E1 n e2 n e3 = .

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