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The prediction intervals proposed by J. F. Lawless (1971) and G. S. Lingappaiah (1973) for the exponential distribution are both simple to use. In this note, we make a comparison of these two prediction intervals based on the expected width of the prediction interval, as well as by means of the probability of the width of one being smaller than the other. For the computation of the latter, we use an algorithm, which is described briefly in the Appendix. Numerical results of these comparisons are presented for different choices of the parameters involved. Both these comparisons reveal that the prediction interval in is better than that in in that it has smaller expected width, as well as higher probability of having smaller width. Finally, we present an example to illustrate the results discussed in this paper.