Geodesic
An Approach to Distribution of the Product of Two Normal Variables
Discussiones Mathematicae. Probability and Statistics, Tome 32 (2012) no. 1-2, pp. 87-99.

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The distribution of product of two normally distributed variables come from the first part of the XX Century. First works about this issue were [1] and [2] showed that under certain conditions the product could be considered as a normally distributed.
Keywords: product of normally distributed variables, inverse coefficient of variation, numerical integration, Monte Carlo simulation, combined ratio 
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Seijas-Macías, Antonio; Oliveira, Amílcar. An Approach to Distribution of the Product of Two Normal Variables. Discussiones Mathematicae. Probability and Statistics, Tome 32 (2012) no. 1-2, pp. 87-99. http://geodesic.mathdoc.fr/item/DMPS_2012_32_1-2_a6/

[1] Cecil C. Craig, On the frequency function of xy, Annals of Mathematical Society 7 (1936) 1-15. doi: 10.1214/aoms/1177732541.

[2] L.A. Aroian, The probability function of a product of two normal distributed variables, Annals of Mathematical Statistics 18 (1947) 256-271. doi: 10.1214/aoms/1177730442.

[3] R. Ware and F. Lad, Approximating the Distribution for Sums of Product of Normal Variables. Research-Paper 2003-15. Department of Mathematics and Statistics (University of Canterbury - New Zealand, 2003).

[4] L.A. Aroian, V.S. Taneja and L.W. Cornwell, Mathematical forms of the distribution of the product of two normal variables, Communication in Statistics - Theory and Method 7 (1978) 164-172.

[5] J. Whisart and M.S.Bartlett, The distribution of second order moment statistics in a normal system, Proceedings of the Cambridge Philosophical Society XXVIII (1932) 455-459. doi: 10.1017/S0305004100010690.

[6] L.A. Aroian, V.S. Taneja and L.W. Cornwell, Mathematical forms of the distribution of the product of two normal variables, Communications in Statistics. Theoretical Methods A7 (2) (1978) 165-172. doi: 10.1080/03610927808827610.

[7] S.C. Chapra and R.P. Canale, Numerical Methods for Engineers (McGraw-Hill: New York, 2010).