課程資訊

INTRODUCTION TO PROBABILITY THEORY

98-1

MATH2501

201 31700

1.學士班三年級必修課。 2.內容含馬可夫鏈與泊松過程導論。

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/981ele_probab

1. Random events and Probability: counting, operations, probability space, urn problem, etc
2. Conditional Probability: conditioning, independence, formulae, Baysian, etc.
3. Random Variables and Distributions : rv and distribution function, discrete-type rv , continuous-type rv, joint (multivariate)- type rv, sum and max of i.i.d. rv’s, conditional-type rv, etc
4. Expectation, Variance, and other Macro-values: expected value, formulae, variance and covariance, correlation, conditional expectation, moment generating function, etc
5. Limits Theorems: some inequalities (Markov, Chebyshev, Chernoff, Cauchy-Schwarz), law of large numbers, DeMoirve-Laplace Theorem, Central Limit Theorem, Poisson Limit Theorem, Approximation of binomial distribution, etc.
6. Poisson Process: inter-arrival and waiting times, Poisson v.s. exponential distributions, compound Poisson process(optional)
7. Finite-state Markov Chain: Random walk, Markov property, Markov matrix, Chapman-Kolmogorov equation, state-classification, invariant distribution, continuous-time MC ( the last three are optional)

To be familiar with basic probability and stochastic process, toward interest in random phenomena.

Course prerequisite：
Calculus, Linear algebra, and some Ordinary Differential Equations (for 6 and 7, optional)

Mid-term: 1-4 of the content, 40 %
Final: 4-7 of the content, 40 %
Homework, 20%

Office Hours

Lecture Notes by N.-R. Shieh

Lecture Notes by N.-R. Shieh
(the 2009 version is in CEIBA for registered students; old version in personal
homepage)
R. Durrett: The Essentials of Probability
R. Durrett: Essentials of Stochastic Processes (Chapters 1 and 3)
S. Ross: A First Course in Probability, the 5th or newer Edition (the newest is the 8th).

(僅供參考)

 No. 項目 百分比 說明 1. Mid-term: 1-4 of the content 40% 2. Final: 4-7 of the content, 40% 3. Homework, Quiz 20%

 課程進度
 週次 日期 單元主題 第3週 9/29,10/01 Quiz 1 第5週 10/13,10/15 Quiz 2 第7週 10/27,10/29 Quiz 3 第9週 11/10,11/12 Mid-term exam at 11/12 第12週 12/01,12/03 Quiz 4 第14週 12/15,12/17 Quiz 5 第16週 12/29,12/31 Quiz 6 第1-17週 2009/09/14--2010/01/08 Lecture Notes by N.-R. Shieh (the 2009 version is in CEIBA for registered students, will post from 2009/09/01). Reference answers for homework 第2-18週 2009/09/22-2010/01/15 Special homework to non-math students