Akademik Dersler - İçerik

Will be able to explain the fundamental concepts of probability theory.
Defines the concepts of sample space and events.
Explains operations on events.
States the classical and axiomatic definitions of probability.
Explains the fundamental properties of probability measures.
Will be able to use the concepts of conditional probability and independence.
Defines and computes conditional probability.
Explains the concept of independent events.
Applies the law of total probability.
Applies Bayes theorem.
Will be able to explain the concept of random variables and types of distributions.
Defines discrete and continuous random variables.
Explains the distribution function.
Explains the probability mass function and probability density function.
Will be able to use the concepts of expected value and moments.
Computes the expected value.
Computes the variance.
Explains higher moments.
Uses the fundamental properties of the expected value.
Will be able to analyze fundamental probability distributions.
Explains Bernoulli and binomial distributions.
Explains geometric and Poisson distributions.
Explains uniform, exponential, and normal distributions.
Will be able to analyze multivariate random variables and their distributions.
Explains the concept of joint distributions.
Obtains marginal distributions.
Computes conditional distributions.
Explains the concept of independence in the multivariate case.
Will be able to explain fundamental limit theorems.
States the law of large numbers.
Explains the central limit theorem.
Will be able to explain sequences of random variables and convergence concepts.
Explains the concept of convergence in probability.
Explains the concept of almost sure convergence.
Applies these concepts in simple examples.