The aim of the present paper is to study the distribution of the mixed sum of two random variables. Here we establish a theorem which gives the probability density function (pdf) of sum of doubly infinite and finite independent random variables. The distribution of the infinite and finite independent random variables is given in the form of corollary. As an application of these results we have obtained a distribution of sum of bilateral exponential variate with triangular, Rayleigh with uniform and Weibull with triangular variate. Some graphs of these distributions have also been given.
On the Mixed Sum of Doubly Infinite and Finite Independent Random Variables,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 3,
2, Article 1.
Available at: https://digitalcommons.pvamu.edu/aam/vol3/iss2/1