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This paper examines the relationship between 1) distributions which have monotonic or bathtub shaped failure rates and 2) the exponential distribution. A method of representing random variables having monotonic or bathtub-shaped failure rate functions as transformations of the exponential and uniform distribution is given. These distributions can thus be simulated using a random number generator. A further application to the mathematical theory could be made by using such transformations of multivariate distributions to define various multivariate nonparametric classes of life distributions.