Probability and Statistics I
| Course Purpose |
|---|
| The purpose of this course is for students to acquire further knowledge and the sills of probability theory and statistical science, based on knowledge given in the course of fundamental probability and statistics. |
| Learning Goals |
| Students will be able to 1. acquire the knowledge on the probability distribution of multi-dimensional random variables, 2. use multi-dimensional calculus to study the probability of continuous random vectors, and 3. acquire the knowledge of the Baysian statistics and apply probability theory to it. |
| Topic | |
|---|---|
| Session 1 | A review of discrete distributions. About the generating function. |
| Session 2 | On multivariate random variables, their joint distribution, and independence. |
| Session 3 | Partitioning formula for conditional expected value and its application. |
| Session 4 | Covariance and correlation coefficient, covariance matrix, and test. |
| Session 5 | An example of continuous distribution. Calculating the mean and variance of specific distributions. |
| Session 6 | Continuous multivariate random variables and their joint density functions. |
| Session 7 | Independence of continuous multivariate random variables. |
| Session 8 | Multidimensional normal distribution, test. |
| Session 9 | Transformation of continuous random variables and their distribution, moment generating function. |
| Session 10 | Distribution of the sum of independent random variables, Poisson process. |
| Session 11 | Limit theorem. Law of large numbers. |
| Session 12 | Starling's formula and the law of large numbers, test. |
| Session 13 | Relationship between central limit theorem and the law of large numbers. |
| Session 14 | Application of central limit theorem. |