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 | Probability spaces, conditional probability, partitioning formula |
| Session 2 | Countable additivity of probability, independence, random variables, expected value |
| Session 3 | Expected value of random variables, variance, Bernoulli distribution, binomial distribution |
| Session 4 | Poisson distribution, geometric distribution, negative binomial distribution |
| Session 5 | Distribution of continuous random variables, distribution functions and density functions, quiz 1 |
| Session 6 | Examples of continuous random variables, uniform distribution, exponential distribution, normal distribution |
| Session 7 | Memorylessness of the exponential distribution, standard normal distribution and normal distribution, calculation of expected value |
| Session 8 | Review of Chapters 3 and 5, moment generating functions, introduction to Chapter 6 |
| Session 9 | Covariance, correlation coefficient, covariance matrix, expectation and variance for the sum of independent random variables, quiz |
| Session 10 | Covariance, the distribution of the sum of independent random variables |
| Session 11 | Analogy with Chapter 4 for continuous sequences of random variables |
| Session 12 | Distribution of the sum of independent continuous random variables, convolution |
| Session 13 | Central limit theorem and its relation to the law of large numbers |
| Session 14 | Application of the central limit theorem |