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In this paper we study the distribution of a product of two continuous randomvariables. We derive formulas for the probability density functions and momentsof the products of the Gaussian, log-normal, Student's t and Pareto randomvariables. In all cases we analyze separately independent as well as correlatedrandom variables. Based on the theoretical results we use the general maximumlikelihood approach for the estimation of the parameters of the product randomvariables and apply the methodology for a real data case study. We analyze adistribution of the transaction values, being a product of prices and volumes,from a continuous trade on the German intraday electricity market.

On the distribution of the product of two continuous random variables  with an application to electricity market transactions. Finite and  infinite-variance case