Hook Method of Integration by Parts and its Applications to Probability Theory

Abstract

Integration of the product of two functions involves steps that are often messy. Tabular methods available in online or in the literature are not that transparent. We present it in a way that the repeated integrals yield a series of parallel lines unless you stop at any step, and the last step yields a hook, and hence the name hook method. We apply it to calculate higher order moments and cumulative probability or survival functions of an exponential random variable related to service times.