Stat400Lec3(Ch1.5)_ans - Chapter 1.5 Independent Events...

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Unformatted text preview: Chapter 1.5 Independent Events What is independence? Properties of independence Pairwise independence does not imply mutual independence Independence Two events A and B are independent if the occurrence of the one does not affect (change) the occurrence of the other. This means P(A|B) = P(A) and P(B|A) = P(B). Example: Grandmas age and grade on midterm are independent events. Your attendance at STAT400 and your final grade in Bio 200 are independent events. This is completely different from the idea of events that are disjoint. Example: Artificial pond Artificial pond with 10 male and 10 female frogs. A = { the first frog is male }, B = { the second frog is male}. (1) If you did not put the first frog back to the pond, P(B|A): the probability of picking up another male frog on your second capture is now less than 0.5 (9/19 or 0.47) successive picks are not independent. (2) If you put the first picked frog back into the pond, the probability of picking a male the second time is just the same as the first time successive picks are independent. P(B|A)=P(B) and we have P(A and B)=P(B)P(A) Examples Let P(A)=0.4 and P(B)=0.5. Compute that P(A B) when A and B are independent. P(A B)= P(A) + P(B) P(A B) = 0.4+0.5-0.4 0.5=0.7 P(A B) when A and B are disjoint. P(A B) = P(A) + P(B) =0.9 P(A|B) when A and B are independent....
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This note was uploaded on 03/14/2012 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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Stat400Lec3(Ch1.5)_ans - Chapter 1.5 Independent Events...

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