ABSTRACT

If X and Y are independent continuous random variables, then the distribution of the sum Z = X + Y is given by

( ) ( )( )h z f x g z x dx ∞

= −∫

(5.1)

where f(x) is the probability density function of X g(y) is the probability density function of Y h(z) is the probability density function of Z

The distribution h(z) is known as the convolution of f(x) and g(y), and is sometimes written as h(z) = f(x)*g(y). Bolch, Greiner, de Meer, and Trivedi (1998, p. 32); Haight (1981, p. 148); Hoel, Port, and Stone (1971, p. 146); Hillier and Lieberman (1980, p. 369); Ross (2003, p. 58); Wolff (1989, p. 25).