APPLICATIONES MATHEMATICAE 36,4 (2009), pp. 419–439 Mridula Garg (Jaipur) Sangeeta Choudhary (Jaipur) Saralees Nadarajah (Manchester) ON THE PRODUCT OF TRIANGULAR RANDOM VARIABLES Abstract. We derive the probability density function (pdf) for the prod- uct of three independent triangular random variables. It involves consid- eration of various cases and subcases. We obtain the pdf for one subcase and present the remaining cases in tabular form. We also indicate how to calculate the pdf for the product of n triangular random variables. 1. Introduction. The triangular distribution is often used when no or little data is available. It is very popular for modelling a subjective esti- mate of some uncertain quantity in business risk models. One of its earliest applications is to model the average number of defects in a chip (Murphy [11]). It is also used in oil and gas exploration where data is expensive to collect and it is almost impossible to model the population being sampled accurately. The triangular distribution, along with the beta distribution, is also widely used in project management. The symmetric triangular dis- tribution is commonly used in audio dithering, where it is called TPDF (Triangular Probability Density Function). Johnson [7] explores the advan- tages of using the triangular distribution as a proxy for the beta distribution. Amaral-Turkman and Gon¸calves [1] add some new applications of triangu- lar and trapezoidal distributions in the genome analysis, particularly, in the construction of physical mapping of linear and circular chromosomes. Re- cent popularity of the triangular distribution can be attributed to its use in discrete system simulation [2], Monte Carlo simulation technique [18] and in standard uncertainty analysis software, such as @Risk (developed by the Palisade Corporation) or Crystal Ball (developed by Decision Engineering). 2000 Mathematics Subject Classification : 33C90, 62E99. Key words and phrases : triangular random variable. DOI: 10.4064/am36-4-3 [419] c  Instytut Matematyczny PAN, 2009