Course Topics
Probability Theory
鈥 Fundamentals of probability: events and sample space. Definition of probability.
鈥 Kolmogorov鈥檚 axioms and probability spaces.
鈥 Combinatorics and counting.
鈥 Conditional probability and independence.
鈥 Law of total probabilities and Bayes鈥 theorem.
鈥 Random variables and probability distributions.
鈥 Expected value and variance. Moments of a random variable. Quantiles and percentiles.
鈥 Common random variables: discrete random variables.
鈥 Common random variables: continuous random variables.
鈥 Functions of a random variable.
鈥 Bivariate random variables: joint and marginal distributions.
鈥 Bivariate random variables: conditional distributions and independence. Covariance and correlation.
鈥 Convergence of sequences of random variable and limit theorems.
Statistical Inference
鈥 Descriptive statistics.
鈥 Populations and their parameters.
鈥 Random sampling. Statistics and Sampling distributions .
鈥 Fundamentals of point estimation. Properties of point estimators.
鈥 Point estimation of the mean and the variance.
鈥 Interval estimation: introduction.
鈥 Confidence interval for the mean and the variance.
鈥 Hypothesis testing: introduction.
鈥 Hypothesis testing: the p-value, type I and II errors. Power and size.
鈥 Hypothesis testing for the mean.
鈥 Hypothesis testing for the difference of two means.
鈥 Chi-squared type tests for contingency tables.
鈥 Estimation methods: method of moments; Maximum likelihood; Least squares.
The linear regression model
鈥 Introduction and assumptions
鈥 Parameter estimation.
鈥 Hypothesis testing and confidence intervals for the parameters of the model.
鈥 Model selection and goodness of fit.
鈥 Residuals analysis and diagnostics.
鈥 Violation of the assumptions and some extensions.
Laboratory
鈥 Introduction to R
鈥 Probability and statistics with R
Teaching format
In person lectures, exercises, lab sessions