MATE-2510 Probability (Honors)

Probability Spaces. Counting, permutations, combinations, multinomial coefficients, sample space, events, probability axioms, equally likely events, probability as a continuous function, as a measure of credibility, conditional probability, Bayes’ formula, independent events, P(.|F) is a probability, random variables (r.v.), discrete variables, expected value, expectancy of a r.v. function, variance, Bernoulli and Binomial, Poisson, other discrete variables, accumulated distribution function, continuous random variables, expectancy and variance, uniform, normal, exponential, other continuous variables, distribution of a function of a random variable, joint distributions, independent random variables, sum of independent r.v., conditional distribution, order statistics, joint probability of the function of a r.v., sum expectancy, moments of the number of events, covariance, correlations, conditional expectancy and prediction, moment generating functions, normal multivariate, weak law of large numbers, central limit theorem, strong law of large numbers.