# Sum, Product and Ratio for the Normal and Student’s **t** Random Variables

**t**

## Abstract

The distributions of the sum \(X+Y\), product \(XY\), and ratio \(X/Y\), when \(X\) and \(Y\) are independent random variables and belong to different families, are of considerable importance and current interest. These have been recently studied by many researchers, (among them, Nadarajah (2005b, c, d) for the linear combination, product and ratio of normal and logistic random variables, Nadarajah and Kotz (2005c) for the linear combination of exponential and gamma random variables, Nadarajah and Kotz (2006d) for the linear combination of logistic and Gumbel random variables, Nadarajah and Kibria (2006) for the linear combination of exponential and Rayleigh random variables, Nadarajah and Ali (2004) for the distributions of the product \(XY\) when \(X\) and \(Y\) are independent Laplace and Bessel random variables respectively, Ali and Nadarajah (2004) for the product and the ratio of t and logistic random variables, Ali and Nadarajah (2005) for the product and ratio of t and Laplace random variables, Nadarajah and Kotz (2005b) for the ratio of Pearson type VII and Bessel random variables, Nadarajah (2005c) for the product and ratio of Laplace and Bessel random variables, Nadarajah and Ali (2005) for the distributions of \(XY\) and \(X/Y\), when \(X\) and \(Y\) are independent Student’s and Laplace random variables respectively, Nadarajah and Kotz (2005a) for the product and ratio of Pearson type VII and Laplace random variables, Nadarajah and Kotz (2006a) for the product and ratio of gamma and Weibull random variables, Shakil, Kibria and Singh (2006) for the ratio of Maxwell and Rice random variables, Shakil and Kibria (2007) for the ratio of Gamma and Rayleigh random variables, Shakil, Kibria and Chang (2007) for the product and ratio of Maxwell and Rayleigh random variables, and Shakil and Kibria (2007) for the product of Maxwell and Rice random variables, are notable). This chapter studies the distributions of the sum \(X+Y\), product \(XY\), and ratio \(X/Y\), when \(X\) and \(Y\) are independent normal and Student’s *t* random variables respectively.