22. The Imperial Electric Co. makes high-quality portable compact disc players for sale in international and domestic markets. The company operates two plants in the United States, where one plant is located in the Pacific Northwest and one is located in the South. At either plant, once a disc player is assem106 Chapter 2 Random Variables, Densities, and Cumulative Distribution Functions bled, it is subjected to a stringent quality-control inspection, at which time the disc player is either approved for shipment or else sent back for adjustment before it is shipped. On any given day, the proportion of the units produced at each plant that require adjustment before shipping, and the total production of disc players at the company's two plants, are outcomes of a trivariate random variable, with the following joint probability density function:

f(x, y, z) = S (x + y)e-X 1(0, (0) (x)/(o, 1)(y)/(o, 1)(Z), where x = total production of disc players at the two plants, measured in thousands of units, y = proportion of the units produced at the Pacific Northwest plant that are shipped without adjustment, and z = proportion of the units produced in the southern plant that are shipped without adjustment.