Past researchers have endeavored to examine and ascertain the time that salespeople spend engaged in core and non-core activities. In this study, the time spent by a salesperson on non-core activities is called vacation time. This study examines the number of times a salesperson engages in vacation and the time taken by the number of vacations by controlling the number of customers. The one dimensional marginal probability generating (transform), density and cumulative distribution functions of the random variables , and are obtained by controlling the variability of two random variables simultaneously.