Probability theory and mathematical statistics is one of the courses of general education for all majorities. This course aims to investigate some random phenomena and their theory and methods. It has wide applications in many actural fields.
This course includes the probability of a union of events, independence of several events, the multiplication rule for conditional probabilities, the formula of the total probability and Bayes’ Theorem; discrete and continuous one-dimensional random variables and their distributions, distribution functions and functions of one-dimensional random variable; bivariate random variables and their joint distributions and marginal distributions, conditional distributions, the independence among a sequence of random variables, functions of two random variables, expectation and variance, moments of a random variable, covariance and correlation and conditional expectation; the Law of Large Numbers, the Central Limit Theorem; the statistics, distributions of samples, the moment estimates, the maximum likelihood estimates, the interval estimates and parameter hypothesis tests, etc.
This study will supplement students some good mathematical methods to investigate and analyze some problems and will make some necessary foundation for the study of some forthcoming courses.