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02_Probability_part1

# 02_Probability_part1 - Chapter 1 Question Ch1~6 p.1 There...

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NTHU MATH 2820, 2008, Lecture Notes Ch1~6, p.1 Chapter 1 Question There are many random phenomena ( example? ) in our real life. What is the language/mathematical structure that we use to depict them? Outline ¾ sample space ¾ event ¾ probability measure • conditional probability • independence ¾ three theorems • Multiplication Law • law of total probability • Bayes’ rule made by Shao-Wei Cheng (NTHU, Taiwan) Ch1~6, p.2 Definition (sample space, TBp. 2) Question What are the differences between the Ω in these examples? Example 1.1 (throw a coin 3 times, TBp. 35) Example 1.2 (number of jobs in a print queue, Ex. B, TBp. 2) Example 1.3 (length of time between successive earthquakes, Ex. C, TBp. 2) A sample space is the set of all possible outcomes in a random phenomenon. = { hhh, hht, hth, thh, htt, tht, tth,ttt } = { 0 , 1 , 2 ,... } = { t | t 0 } Ω is a finit set Ω is an infinite, but countable, set Ω is an infinite, but uncountable, set

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02_Probability_part1 - Chapter 1 Question Ch1~6 p.1 There...

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