Problems in probability theory, mathematical statistics and theory of random functions

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Joint distribution function of X and Y ,defined as. It means for every possible combination of random variables X, Y we represent a probability distribution over Z.

Experiments, sample space, events, and equally likely probabilities

There are a number of operations that one can perform over any probability distribution to get interesting results. Some of the important operations are as below. Marginalisation This operation takes a probability distribution over a large set random variables and produces a probability distribution over a smaller subset of the variables. This operation is known as marginalising a subset of random variables. This operation is very useful when we have large set of random variables as features and we are interested in a smaller set of variables, and how it affects output.

Problems in probability theory, mathematical statistics and theory of random functions

For ex. The set of input random variables are called scope of the factor. For example Joint probability distribution is a factor which takes all possible combinations of random variables as input and produces a probability value for that set of variables which is a real number. Factors are the fundamental block to represent distributions in high dimensions and it support all basic operations that join distributions can be operated up on like product, reduction and marginalisation.

Factor Product We can do factor products and the result will also be a factor. Sign in.

Persons: Shiryaev, Albert Nikolaevich

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Study the probabilistic-statistical methods that will further allow studying of more specialized subjects, based on probabilistic models. The course covers the following topics: the probability of random events; a sequence of independent trials; random variables; numerical characteristics of random variables; the law of large numbers; characteristic functions of random variables; Markov chain; stochastic processes.

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