Instructional goals
Aim of the course is to provide a solid background in probability and mathematical statistics, possibly with . a first approach to computational statistical software.
Prerequisites
A basic background in calculus and linear algebra is required.
Intended learning outcomes
Course Contents
1. Probability spaces: axiomatic approach and uniform spaces. Fundamentals of combinatorics
2. Conditional probability and independence.
3. Discrete random variables: binomial, geometric and hypergeometric.
4. Continuous random variables: uniform, Normal and exponential.
5. Expectation, variance, moments and moment generating function.
6. Joint distributions, independence of random variables, Gamma distributions,
covariance and correlation coefficients.
7. Conditional mean and variance.
8. Limite theorems: the law of large numbers, the central limit theorem, normal approximation.
9. Sampling.
10. Point estimation: maximum likelihood estimators, method of moments.
11. Hypothesis testing.
12. Interval estimation.
13. Linear regression.
Reference Books
[CB]
G. Casella
R.L. Berger
Statistical inference
ed. Duxbury
[BH] J. K.Blitzstein-
J. Hwang
Introduction to Probability
ed. Chapman & Hall
Lecture notes
Teaching Methods
Lessons and recitation classes possibly also using some computational software
Assessment Method
Written midterm and final exam, as a test and/or a project
Thesis assignment criteria
A good performance in the course
Does the syllabus cover sustainability topics?
no
Week 1 Contenuto sessioni on line e on campus
Beginning in the second week
Week 2 Contenuto sessioni on line e on campus
Probability spaces: axioms, uniform probability spaces, combinatorics
Conditional probability and independence.
Discrete random variables: binomial, geometric and hypergeometric.
[BH] chapters 1,2, 3
Week 3 Contenuto sessioni on line e on campus
Continuous random variables: uniform, Normal and exponential r.v.’s.
[BH] chapter 5: 5.1-5.5
Week 4 Contenuto sessioni on line e on campus
Expectation, variance, moments and moment generating function.
[BH] chapter 4: 4.1, 4.2, 4.6, chapter 6: 6.1-6.6
Week 5 Contenuto sessioni on line e on campus
Joint distributions, independence of random variables, Gamma distributions,
covariance and correlation coefficients. Univariate and multivariate Gaussian distribution
[BH] chapter 7: 7.1, 7.3, chapter 8: 8.1, 8.4
Week 6 Contenuto sessioni on line e on campus
Conditional mean and variance.
[BH] cap. 9: 9.1-9.5
Week 7 Contenuto sessioni on line e on campus
Limite theorems: the law of large numbers, the central limit theorem, normal approximation.
[BH] cap. 10
Week 8 Contenuto sessioni on line e on campus
Sampling.
[CB] cap. 5: 5.1-5.4
Week 9 Contenuto sessioni on line e on campus
Point estimation: maximum likelihood estimators, method of moments.
[CB] cap. 7: 7.1, 7.2.1, 7.2.2, 7.3.1, 7.3.2
Week 10 Contenuto sessioni on line e on campus
Hypothesis testing.
[CB] cap. 8: 8.1, 8.3.1, 8.3.2, 8.3.4
Week 11 Contenuto sessioni on line e on campus
Interval estimation. Confidence intervals
[CB] cap. 9: 9.1, 9.2.1, 9.2.2, 9.2.3
Week 12 Contenuto sessioni on line e on campus
Linear regression.
[CB] cap11: 11.1, 11.3