93264 - Introductory Statistics

Learning outcomes

This is an optional introductory course in statistics for newly-admitted LMEPP students whose statistics background is not strong enough for the LM level. Upon admission, the admissions committee may recommend students to take this course. At the end of the course, students master the minimal statistics background that is needed to succeed in the more advanced statistics and econometrics courses offered at LMEPP.

Course contents

• Discrete probability: Random trial, event, sample space; Kolmogorov axioms; Conditional probability, chain rule, tree diagram; Independent events; Law of total probability; Bayes' theorem.
• Discrete random variables: Probability mass function, cumulative function; Main distributions (uniform, binomial, Poisson…); Moments of a distribution; Expected value and variance; Random vectors, joint distribution, correlation.
• Continuous random variables: Probability density function (PDF), Chebishev's inequality; Main PDFs (uniform, normal, exponential…); Bivariate distributions.
• Fundamental theorems: Law of large numbers; Central limit theorem.
• Point estimation: Method of moments; Maximum likelihood estimators; Bias.
• Confidence intervals: Mean and variance estimation  for normal cases; Asymptotic normality; Chi-squared and Student's t distributions.
• Hypothesis test: Significance level; Confusion matrix; Mean and variance in normal samples; Samples comparison.
• Linear regression: Bivariate samples; Covariance; Linear regression coefficients; Least squares method; Pearson's and Spearman's coefficients; Introduction to non-linear regression.

The order in which the topics are covered is only indicative and may vary.

Readings/Bibliography

Reference textbooks:

• S. ROSS, "Introduction to Probability and Statistics for Engineers and Scientistis", University of California
• J. WOOLRIDGE, "Introductory Econometrics - A modern approach", Cengage Learning

Only limited sections of the textbooks will be actually studied.

Teaching methods

Lectures, delivered partly online and partly in person. Students are encouraged to participate actively in the lectures, asking questions during class and taking part in solving the exercises.

Assessment methods

The final examination consists of a 2-hour written test.

The test involves both solving simple exercises, similar to those covered in class, and answering short-answer theoretical questions.

The use of a scientific calculator is allowed during the test.

Teaching tools

Course handouts, support material and links, notes taken during lessons and exercise sheets will be made available on Virtuale.

Office hours

See the website of Mattia Vincenzo Edoardo Massone