Theory of Probability& Mathematical Statistics
Course Number: 10525
Study Period: Aug. 2009-Nov. 2009
Study Load: 4 lessons/week, 48 Class Hours ,3 Credits
Test book: Theory of Probability& Mathematical Statistics, authored by LI Yaqiong, published by Fudan University Press
Prerequisite course: Calculus, Linear Algebra
Evaluation and Grades:
Work: Assignments; Allocation: 20%
Work: Final Exam; Allocation: 80%
Unit 1 Introduction (6 Class Hours)
【 Master 】
Random Event;
Probability;
Event independence;
Unit 2 Random variable and Distribution (8 Class Hours)
【 Master 】
Random variable, Distribution function; Discrete random variable; Concrete random variable;
Unit 3 Multi-dimensional random variable and Probability distribution (10
Class Hours)
【 Master 】
Two-dimensional random variable and probability distribution;
Continuous joint probability density, Edge density;
Independence of random variables;
Two-dimensional uniform distribution, Two-dimensional normal distribution;
Simple function of two random variables;
Unit 4 Digital features (8 Class Hours)
【 Master 】
Mathematical expectation, variance, standard deviation, covariance, correlation coefficient, moment; Binomial distribution, Poisson distribution, uniform distribution, normal distribution, exponential distribution;
Chebyshev inequality
Unit 5 Law of large numbers and central limit theorem
(3 Class Hours)
【 Master 】
Chebyshev Law of large numbers, Bernoulli Law of large numbers, Khinchine Law of large numbers;
DeMoivre-Laplace central limit theorem, Levy-Lindeberg central limit theorem;
Unit 6 Sample and Sampling distribution (4 Class Hours)
【 Master 】
Statistical Population, Simple random sampling;
χ2 distribution, t-distribution and F distribution;
Normal distribution;
Unit 7 Parameter estimation (5 Class Hours)
【 Master 】
Point estimation; estimator, moment, Maximum Likelihood;
Unbiased estimator, effectiveness (minimum variance of) and consistency (consistency);
Interval Estimation;
Unit 8 Hypothesis testing (4 Class Hours)
【 Master 】
The process of hypothesis testing, the two errors of hypothesis testing;
