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¥ $1#'¢ Independence
Does knowing that one event has occured alway have
an impact on the probability of another event?
? DEFINITION: (Def. 3.9, p. 131) Events and are said to be independent if or get an even number “Not independent” = “DEPENDENT.” # greater than 3 Ex. Die Toss: ¥ and DEPENDENT,
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¨¦¥'&%6#¤¦¥¤¢ EXAMPLE : Toss a balanced die. 21#'&¨¥ r1#¤¢
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'¢ If it lasts through its ﬁrst use, prob. that it lasts a year ¥
¦ fail on ﬁrst use Note that if and are independent then
[by Mult. Law]
[by independence] 80 STA 2023 c B.Presnell & D.Wackerly  Lecture 6 STA 2023 c B.Presnell & D.Wackerly  Lecture 6 81 Ex. (LAST TIME!!!) Odds are 2:1 that when H and T This is another way to deﬁne independence: (p. 133) and winner of each recorded.
Odds are 2:1 that H wins means H wins with prob. ` ¢iF§ 1H£ ¢H
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3 WARNING . T wins with prob. ` 21#'
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§ £ ¢§ £ ¢ © § 4 £ Independent play racquetball, H will win. H and T play 3 matches, . Probs. given Do NOT confuse INDEPENDENT with MUTUALLY in the example for 8 possible outcomes were c...
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 Spring '08
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