Probability Theory and Statistics

Sample spaces, events, Probability measures. Conditional Probability, Law of total Probability, Bayes’s formula. Independent events. Elementary Combinatorics. Random variables and their distribution. Special discrete and continuous distributions. Expectation, median, variance, moments. Markov, Chebyshev and Jensen inequalities. Multivariate distributions. Joint, marginal and conditional distributions. Conditional expectation. Independence, measures of correlation. Multidimensional normal distribution. Transformations of random variables and random vectors. Sums/extrema of independent random variables. Law of Large Numbers, Chernoff bounds, Central Limit Theorem. Poisson Processes. Descriptive Statistics. Parameter estimation, bias, Moment Estimator, Maximum Likelyhood Estimator. Confidence intervals.