Checking date: 31/05/2022


Course: 2022/2023

Probability II
(14461)
Study: Bachelor in Statistics and Business (203)


Coordinating teacher: JIMENEZ RECAREDO, RAUL JOSE

Department assigned to the subject: Department of Statistics

Type: Basic Core
ECTS Credits: 6.0 ECTS

Course:
Semester:

Branch of knowledge: Social Sciences and Law



Requirements (Subjects that are assumed to be known)
Probability I
Objectives
1. Understand the concept of random vector: description and applications. 2. Use the concept of correlation. 3. Work with the multivariate normal distribution. 4. Use the limit theorems and asymptotic results in statistical applications. 5. Understand the concept of statistics and its sampling distribution. 6. Obtain the sampling distribution of estimators in normal population and derive the associated confidence intervals. 7. Use computational tools for calculation of confidence intervals. 1. Information Management Skills. 2. Solve Problems independently. 3. To be capable of using creative thoughts when it comes to solve problems. 4. Critical Reasoning.
Skills and learning outcomes
Description of contents: programme
1. Discrete random vectors. 1.1. Joint, marginal and conditional distributions. 1.2. Independence. 1.3. Functions of random vector. 1.4. Expected value, variance, Conditional expectation. 1.5. Discrete multivariate models. 1.6. Markov inequality. Convergence in probability. 1.7. Laws of Large Numbers 1.8. Moments. generating functions. Convergence in distribution 1.9. Moivre┬┐Laplace theorem 2. Continuous random vectors. 2.1. Joint, marginal and conditional distributions. 2.2. Independence. 23. Function of random vector. 2.4 Expected value, variance and conditional expectation. 2.6. Markov inequality. Convergence in probability. 2.7. Laws of Large Numbers 2.8. Moments, generating functions. Convergence in distribution 2.9. Central Limit Theorem 3. Distributions related to Normal distribution. 3.1. Change of variable. 3.2. Two-dimensional and multidimensional normal distribution. 3.3. Chi-square and t-student. 3.4. Fisher's theorem
Learning activities and methodology
Theory (4 ECTS). Lectures with available material posted in internet. Problems (2 ECTS) Problem Solving classes. Work assignments in groups.
Assessment System
  • % end-of-term-examination 0
  • % of continuous assessment (assigments, laboratory, practicals...) 100
Calendar of Continuous assessment
Basic Bibliography
  • Casella, G. y Berger, R.L.. Statistical Inference. Wadsworth and brooks. 1990.
Additional Bibliography
  • Durret, R.. The Essentials of Probability. Duxbury Press. 1994.
  • Grimmett, G. y D. J. A. Welsh.. Probability: An introduction.. Oxford University Press. 2003

The course syllabus may change due academic events or other reasons.