Volume 34 | Number 1 | Year 2016 | Article Id. IJMTT-V34P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V34P507

In this paper, we find the two solutions of a system of two dimensional integral equations contains respectively two beta distributions with different values of the two parameters in two cases and equal in the third that is to introduce two corresponding probability density functions. The variance of each resulting probability density function corresponding to the supposing three cases are derived that is to indicate which of the probability density function gave the maximum variance. Furthermore, the correlation coefficient between any pair of the probability density function is determined.

[1] Balakchandran, K.K., and Kuo H.H., “Existence of Solutions of General Nonlinear Stochastic Voltera Fredholm Integral Equations”, Stochastic Analysis and Applications, Vol.23, pp.827-851, 2005.

[2] Milton, J.S. and Padgett, W.J., ”On The Existence and Uniqueness of Random Solution to a Perturbed Random Integral Equation of the Fredholm Type”, SIAM J. Applied Math., Vol.22, pp.194-208, 1972.

[3] Huda, H.O., “Solutions for the Generalized Multi- Dimensional Voltera Integral and Integro Differential Equations”, MSc. Thesis, College of Education, Ibn Al- Haitham, Baghdad University, Iraq, 2007.

[4] Vahidi, A.R. and Mokhtari, M., “The Decomposition Method for System of a Linear Fredholm Integral Equations of the Second Kind”, Applied Mathematical Sciences, Vol.2, pp.57-62, 2008.

[5] Biazar, J. and Rangbar, A., “A Comparison Between Newton’s Method and Adomian Decomposition Method for Solving Special Fredholm Integral Equations”, Int.Math.Forum, Vol.2, pp.215-222, 2003.

[6] Abbaoui, K. and Cherruault, Y., “Convergence of Adomian’s Method Applied to Differential Equations”, Math.1 Comput. Modeling, Vol.28, No.5, pp.103-110, 1994.

Mohammad Wahdan Muflih, Areej Salah Mohammad, Ahmed Issa Abdulnabi, "Some Statistical Properties of the Solutions of a
System of two dimensional Integral Equations
contains Beta distribution," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 34, no. 1, pp. 28-33, 2016. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V34P507