Abstract
Fundamental methods are developed for the derivation of the probability density function and moments of rational algebraic functions of independent random variables. Laplace and Mellin integral transforms have been used to obtain the probability distribution of such elementary functions involving arithmetic operations of sum, difference, product and quotient. In dealing with these operations on independent random variables, it is necessary to obtain the conversion of the Laplace transform to the Mellin transform and vice versa. Two theorems establishing the relationship between Laplace and Mellin transforms have been proved. Examples of the application of the method to problems in engineering and business analysis have been provided.
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