IND 252E - Olasılık Teorisi

Dersin Amaçları

Making a basic introduction to the Theory of Probability which is an
important foundation of Industrial Engineering. Showing possible
applications, in addition to the theoretical presentation of the subjects,
through examples.

Dersin Tanımı

Combinatorial analysis: counting, permutation, combination, binomial and multinomial coefficients, number of non-negative and positive integer solutions of a linear equation. Definition of probability and related concepts, different approaches to probability, axioms of probability, sample spaces having equally likely outcomes. Conditional probability, Bayes’ theorem, independent events. Random variables, distribution functions, expected value and variance. Discrete random variables: discrete uniform distribution, Bernoulli and related distributions, Poisson distribution, hypergeometric distribution. Continuous random variables: uniform distribution, normal distribution, exponential distribution, distribution of a function of a random variable. Jointly distributed random variables, sums of independent random variables, conditional distributions, order statistics, distribution of functions of random variables. Conditional expectation, moment generating functions. Limit theorems: Chebychev's inequality, the central limit theorem. Some computer applications.