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- W85273309 abstract "This chapter discusses the functions of random variables. In the special case of one-dimensional vectors, Y and Z formulae determine the expectations and second-order moments of scalar functions of random variables. In the general case for finding the expectations and second-order moments of nonlinear functions of random variables, it is necessary to know the density of random variables-arguments. The complexity of calculations of expectations, variances, and covariances of nonlinear functions of random variables leads to the natural desire to forgo exactness for the sake of simplicity and to find simple approximate formulae similar to the formulae for the moments of linear functions of random variables. To establish such approximate formulae, the linearization method is usually used that consists in replacing nonlinear functions by linear ones sufficiently close to them. In many practical problems, especially in mathematical statistics, it is necessary to know how to find the distribution of a function of a random variable. The probability of occurrence of the random variables Y = φ ( x ) in a set B is equal to the probability of occurrence of the random variables X in set A B = { x : φ ( x ) ∈ B }." @default.
- W85273309 created "2016-06-24" @default.
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- W85273309 date "1984-01-01" @default.
- W85273309 modified "2023-09-24" @default.
- W85273309 title "FUNCTIONS OF RANDOM VARIABLES" @default.
- W85273309 doi "https://doi.org/10.1016/b978-0-08-029148-2.50009-4" @default.
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