5章机率论.pptVIP

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. 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 six 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 Numbers 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 10,000 times and then computing the relative frequency of heads 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 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 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 * * * * 林惠玲 陳正倉著 雙葉書廊發行 2004 統計學 方法與應用 第5章 機率論 * 第5章 機率論 學習目的 本章結構 隨機實驗 表5.1 隨機實驗、出