98年第1學期-4344 高等機率 課程資訊

評分方式

評分項目	配分比例	說明
期中考	50
期末考	50

教育目標

(1)Measure and Probability (2)Random variables (3) Independence (4)Expectation (5)Convergence of stochastic process (6)Conditional expectation (7)Martingales

課程概述

Contents 1. Measure and Probability 1.1. Measure and Probability 1.2. Lim sup and lim inf 1.3. -algebra 1.4. Probability measure 1.5. Home exercises 1.6. Ans. Home exercises 2. Random variables 2.1 Random variable 2.2 Operations of random variables 2.3 Distribution function 2.4 Vector random variables 2.5 Home exercises 2.6 Ans. Home exercises 3. Independence 3.1. Independent 3.2. Independent random variables 3.3. Bernoulli and Poisson process 3.4. Bernoulli and Random walk 3.5. Home exercises 3.6. Ans. Home exercises 4. Expectation 4.1 Step functions and expectation 4.2 Positive random variable and Fatou’s lemma 4.3 Integrable random variables 4.4 - space and inequality 4.5 Distribution and its integral 4.6 Home exercises 4.7 Ans. Home exercises 5. Convergence of stochastic process 5.1. Convergence of stochastic process 5.2. Positive random variables and Fatou’s lemma 5.3. Intergrable random variables 5.4. - space and inequality 5.5. Distribution and its integral 5.6. Home exercises 5.7. Ans. Home exercises 6. Conditional expectation 6.1 - space and projection theorem 6.2 Conditional expectation random variable 6.3 Application of expectation random variable 6.4 Home exercises 6.5 Ans. Home exercises 7. Martingales 7.1 Discrete time martingales 7.2 Stopping times 7.3 Optional sampling theorem 7.4 Martingale convergence theorem 7.5 Home exercises 7.6 Ans. Home exercises.

基本資料

必選課，學分數：3-0
上課時間：五/2,3,4[ST516]
修課班級：數學碩1,2
修課年級：年級以上
選課備註：[人工選課]甲組

參考書目

葉老師講義