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1、第5章 機率論,學習目的,本章結構,Definitions,A probability is a measure of the likelihood that an event in the future will happen. It it can only assume a value between 0 and 1. A value near zero means the event is not likely to happen. A value near one means it is likely.,表5.1 隨機實驗、出象與樣本空間,隨機實驗的基本觀念,圖5.1 擲一個銅板兩次的
2、樣本空間,隨機實驗的基本觀念,圖5.2 簡單事件與複合事件,機率理論,Classical Probability,Consider an experiment of rolling a six-sided die. What is the probability of the event “an even number of spots appear face up”? The possible outcomes are: There are three “favorable” outcomes (a two, a four, and a six) in the collection of s
3、ix equally likely possible outcomes.,Empirical Probability,The empirical approach to probability is based on what is called the law of large numbers. The key to establishing probabilities empirically is that more observations will provide a more accurate estimate of the probability.,Law of Large Num
4、bers,Suppose we toss a fair coin. The result of each toss is either a head or a tail. If we toss the coin a great number of times, the probability of the outcome of heads will approach .5. The following table reports the results of an experiment of flipping a fair coin 1, 10, 50, 100, 500, 1,000 and
5、 10,000 times and then computing the relative frequency of heads,圖5.3 投擲銅板出現正面的機率,Subjective Probability - Example,If there is little or no past experience or information on which to base a probability, it may be arrived at subjectively. Illustrations of subjective probability are: 1. Estimating the
6、 likelihood the New England Patriots will play in the Super Bowl next year. 2. Estimating the likelihood you will be married before the age of 30. 3. Estimating the likelihood the U.S. budget deficit will be reduced by half in the next 10 years.,Summary of Types of Probability,機率的公理,19,Counting Rule
7、s Multiplication,The multiplication formula indicates that if there are m ways of doing one thing and n ways of doing another thing, there are m x n ways of doing both. Example: Dr. Delong has 10 shirts and 8 ties. How many shirt and tie outfits does he have? (10)(8) = 80,20,Counting Rules Multiplic
8、ation: Example,21,Counting Rules - Permutation,A permutation is any arrangement of r objects selected from n possible objects. The order of arrangement is important in permutations.,22,Counting - Combination,A combination is the number of ways to choose r objects from a group of n objects without re
9、gard to order.,事件機率,表5.2 事件的聯合（聯合次數分配）,表5.3 聯合機率分配表,表5.4 汽車墊片的品質與模具狀況分析表,表5.5 汽車墊片的品質與模具狀況的機率表,圖5.4 汽車墊片的品質與模具狀況的樹枝圖,表5.6 一般化的聯合機率分配表,圖5.5 事件A的條件機率 圖5.6 事件B的條件機率,表5.7 台北與紐約股市關聯表,表5.8 台北與紐約股市漲跌機率表,事件的性質與關係,表5.9 高中應屆畢業生申請參加甄試的結果,表5.10 電機學院甄試結果 表5.11 文學院甄試結果,事件的性質與關係,表5.12 台灣地區就業者之職業及教育程度,貝氏定理,表5.13 新唱片上市成功的機率,表5.14 新唱片上市成功與調查報告,表5.15 上市成功與失敗的聯合機率分配表,圖5.7 貝氏定理的樹枝圖,圖5.8 貝氏定理的應用,
