MAT 221 - Probability Theory

Course Objectives

1. To provide the basic concepts of probability
2. To set up probability models for a range of random phenomena, both discrete and continuous
3. Developing critical thinking skills, and the abilities to apply techniques of calculus (i.e., derivatives, integration, infinite series) to assess the probability of an event.

Course Description

Experiment, sample space, algebra of events, sigma-algebra of events, probability measure on a sigma-algebra, sigma-algebra of borel sets, Kolmogorov axioms, conditional probability. Combinatorial methods; product rule, permutation, combination, binomial expansion, multinomial expansion, tree diagram, Bayes theorem. Random variables. Discrete density functions, probabilities in discrete sample space, equally likely outcomes. Cumulative distribution function. Continuous density functions, probability in continuous sample space. Functions of random variables. Bivariate random vector, bivariate joint density functions, marginal and conditional density functions, independent random variables. Definition and properties of expectations. Special expectations; mean, variance, ovariance and correlation coefficient, Markov and Chebyshev inequality. Moment generating function, computation of moments using moment genering functions. Discrete distributions; Bernolli, Binom, multinomial, geometrik, negatif-Binom ve Poisson distributions. Continuous distributions; Normal, gamma, exponential, Chi-square, t- and F- distributions. Limit theorems; law of large numbers and central limit theorem. Slutsky teorem. Markov chains