# lec14 - STATISTICS 13 Lecture 14 Oct 27, 2010 Review...

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STATISTICS 13 Lecture 14 Oct 27, 2010

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Review Conditional Probability Independence Equivalent definitions
Example: Toss Two Dice Toss two fair dice. A= the sum of two dice is 7 ; B=First die shows a “4” Question: Are A and B independent?

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Example: Toss Two Dice (Cont.) If A=the sum of two dice is 6; B=First die shows a “4”, are they still independent?
Calculation of Probability: Intersection Multiplication rule: For any two events A and B, probability that both A and B occur is P(A B)=P(A|B)P(B) if P(B)>0, also P(A B)=P(B|A)P(A) if P(A)>0 If two events A and B are independent then, P(A B)=P(A)P(B)

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Example: Urn Problem Urn problem: An urn contains three red balls and two yellow balls. Two balls are randomly chosen without replacement , what is the probability that both balls are red? How about balls are chosen with replacement?
Example Toss a fair die twice. What is the probability that exactly one “6” shows up ?

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Random Variables A random variable is a mapping from the sample space S to the real
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## This note was uploaded on 11/18/2010 for the course STA 80760 taught by Professor Jiepeng during the Spring '10 term at UC Davis.

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lec14 - STATISTICS 13 Lecture 14 Oct 27, 2010 Review...

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