Mathematical Statistics

The basic statistics include descriptive statistics and inferential statistics. The former is to organize and to summarize the data in a systematic way so as to reach comprehensive statement for the sample; the latter is to use various measures to characterize the sample and patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and are then used to draw inferences about the process or population being studied. The inferential statistics is the core of the modern statistics and thus this course will emphasize the inferential statistics other than the methods of descriptive statistics. In particular, this course is concerned with the theoretical basis of the statistics using probability theory in order to clearly grasp the major concept of statistics. The mathematical methods will be employed to exemplify (or prove) the important statistical theory.