Probability & Statistics

Spring 2021

• Intro
• Aims
• Contents
• References
• Grading

Introduction

Course objectives

1. Develop a basic intuition and treatment of random phenomena.
2. Understanding and handling of the basic principles in Probability.
3. Study of the basic model distributions in Probability.
4. Understanding of the basic concepts and methods in Descriptive Statistics.
5. Understanding and basic use of the concepts and the methods in Statistical Inference.

Contents

1. Descriptive Statistics.
2. Probability. Intro and basic concepts.
3. Random variables. Expectation. Variance. Some common distributions.
4. Random vectors. Joint distribution. Marginal distribution. Conditional distribution. Independence.
5. Limit theorems Law of Large Numbers. Central Limit Theorem. Distributions related to the Gaussian.
6. Estimation. Basic concepts. Maximun likelihood. Confidence intervals.
7. Tests of Hypothesis. Basic concepts. Tests of hypothesis and confidence intervals: some examples. Tests related to the Binomial and the Normal distibutions. Non parametric tests: "Chi-square" tests.

References

DeGroot, M. H. (1988). Probabilidad y Estadística. Addison-Wesley Iberoamericana.

Grimmett, G.; Welsh, D. (1986). Probability. An Introduction. Oxford Science Publications.

Hoel, P.; Port, S.; Stone, C. (1971). Introduction to Probability Theory. Houghton Mifflin Company.

Hoel, P.; Port, S.; Stone, C. (1971). Introduction to Statistical Theory. Houghton Mifflin Company.

Hogg, R.; Craig, A. (1978). Introduction to Mathematical Statistics. Collier-Macmillan.

de la Horra, J. (2003). Estadística Aplicada. Díaz de Santos.

McClave, J.; Sincich, T. (2011). Statistics. 12th ed. Pearson.

Mendenhall, R. L.; Scheaffer, R. L.; Wackerly, D. D (1986). Estadística Matemática con Aplicaciones. Grupo Editorial Iberoamérica.

Montgomery, D. C.; Runger, G.C. (1996). Probabilidad y Estadística aplicadas a la Ingeniería. McGraw Hill.

Peña, D. (2001). Fundamentos de Estadística. Alianza Editorial.

Peña, D.; Romo, J. (1997). Introducción a la Estadística para las Ciencias Sociales. McGraw-Hill.

Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. (1992). Numerical Recipes in C. Cambridge University Press.

Rice, J. A. (1995). Mathematical Statistics and Data Analysis. Wadsworth & Brooks.

Ross, S. M. (1987). Probability and Statistics for Engineers and Scientists. Wiley.

Scheaffer, R. L.; McClave, J. T. (1993). Probabilidad y Estadística para Ingeniería. Grupo Editorial Iberoamérica.

Trivedi, K. S. (1982). Probability and Statistics with Reliability, Queuing and Computer Science Applications. Prentice-Hall.

Grading system

May 2011 assessment. Two possibilities:

1. Progressive grading:
   • Two mid-terms (P1 ---April, 9th, 9:00-11:00 am--- and P2 ---May, 7th, 9:00-11:00 am) and three assignments (A1, A2, A3).
   • The final grade will be calculated using the following weighted mean:
     Final grade = 0.35 (P1) + 0.35 (P2) + 0.1 (A1) + 0.1 (A2) + 0.1 (A3)
     Students passing the course via the progressive grading do not need to take the final exam.
   Important: in order to pass the course via continuous assessments, a grade of at least 3.5 out of 10 is required in both partial exams and all the assignments.
2. Global examination: The grade obtained in the May final examination (Monday, May 17th).

June 2021 assessment: