If the probability is f(x) that a product fails the xth time it is being used, that is, on the xth trial, then its failure rate at the xth trial is the probability that it will fail on the xth trial given that it has not failed on the first x – 1 trials; symbolically, it is given by Z(x) = f (x) / 1 – F(x– 1) where F(x) is the value of the corresponding distribution function at x. Show that if X is a geometric random variable, its failure rate is constant and equal to θ.
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