Syllabus
Part I. Probability (5 weeks)
Week 1. Cumulative distribution function, mathematical expectation and variance for discrete RV. Bernoulli, binomial and Poisson RVs. Introduction to R. RV computer generation and simulation.
Week 2. Cdf and density of continuous RV, expectation and variance. Examples of continuous RV: uniform and exponential distributions.
Week 3. Normal distribution and its properties. RV generation and simulation in R.
Week 4. Bivariate distribution, coefficient of correlation and conditional distribution, regression as conditional expectation. Several RVs, indepen- dence. Bivariate normal distribution, conditional variance.
Week 5. Several normal variables (multivariate normal distribution), chi- square and t-distributions. The Central Limit Theorem and approximations.
Mid-term exam (take home exam, probability), the beginning of February, just before Winter carnival.
Part II. Statistics (5 weeks)
Week 6. Statistics as an inverse problem of probability. The concept of statistical estimation and method of maximum likelihood and method of moments with examples.
Week 7. Confidence intervals for the means, standard deviation and stan- dard error, confidence level.
Week 8. Regression, least squares estimation. Prediction by regression, multivariate regression.
Week 9. Hypothesis testing, type I and type II errors, statistical signif- icance and p-value, Z-test, unpaired and paired t-test, test on proportions and means.
Team project presentation, the last class.
Final exam (take home exam, statistics only).