29596 - Probability And Statistics

Learning outcomes

Upon successful completion of the 30‑hour module, students will be able to:

1. Formulate rigorous probability models
   Construct an appropriate sample space, σ‑algebra and probability measure for economic phenomena.

2. Translate economic questions into probabilistic statements
   Deploy counting arguments, conditional probability and Bayes’ theorem to evaluate event probabilities in settings such as lotteries, information games and urn models.

3. Analyse random variables and their distributions
   Identify relevant discrete or continuous laws, derive their moments and transforms, and describe joint, marginal and conditional behaviour.

4. Apply large‑sample theory
   State and use the main modes of convergence, justify the Weak/Strong Law of Large Numbers and Central Limit Theorem for simple cases, and employ these results to obtain asymptotic approximations.

5. Derive and assess estimators
   Obtain Method‑of‑Moments and Maximum‑Likelihood estimators, evaluate bias and variance, and determine asymptotic distributions.

6. Construct confidence intervals and conduct hypothesis tests
   Compute/interpret confidence intervals, construct statistical tests

Course contents

1 - Probability and Distribution Theory: Probability foundations: sets, counting & axioms, Conditional probability, Bayes’ rule & independence, Random variables, distribution functions and expectation, Catalogue of standard discrete / continuous distributions, Joint distributions and densities, Independence and dependence of random variables, Conditional distributions and moments, Random vectors

2 - Statistical Inference: Random samples, Sample statistics, Sampling distributions, Modes of convergence of random variables, Law of Large Numbers, Central Limit Theorems

3 - Point and Interval Estimation Theory: Estimators and their finite‑sample properties, Method of Moments, Likelihood and Maximum‑Likelihood Estimation, Interval estimators and confidence regions

4 - Hypothesis Testing: Statistical tests and their operating characteristics, Neyman–Pearson framework, Likelihood‑ratio, Wald and Score tests

Readings/Bibliography

Casella, G. and Berger, R.L. (2002) Statistical Inference. 2nd Edition, Duxbury Press, Pacific Grove.

Abadir, K. M., Heijmans, R. D. H., & Magnus, J. R. (2018). Statistics. Cambridge: Cambridge University Press.

 

Teaching methods

Traditional lectures

Teaching tools

A dedicated Virtuale page will provide access to the selected course materials.

Office hours

See the website of Enzo D'Innocenzo