The objective of this course is to familiarize students with the basic concepts of probability and the most common distributions. This knowledge will be useful not only for future courses of Statistics of Stochastic Processes, but is also directly applicable in many situations where chance or randomness prevail. Combinatory Methods. Binomial coefficients. Sample Spaces. Probability, rules. Conditional probability, independence. Bayes’ Theorem. Probability distributions. . Continuous random variables, density functions. Multivariate distributions. Marginal distributions. Conditional distributions. Expected value. Moments, Chebyshev’s Theorem. Moment generating functions. Product moments. Comb moments. Linear moments, conditional expectation. Uniform, Bernoulli, Binomial. Negative binomial, geometric, hyper-geometric. Poisson. Multinomial, multivariate hyper-geometric. Uniform, gamma, exponential, j-I squared. Beta distribution. Normal distribution. Normal to binomial approximation. Normal bivariate. Functions of random variables. Transformation technique: one variable. Transformation technique: several variables. Moment generating function technique. Sampling distributions. Mean distribution.

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### Instructor

Benitez Castro Ferney