26. Referring to Problem 25, show that P(Y >s+ t|Y >s) = P(Y >t) =

∞

y=t+1 pqy−1.

(This result implies that the geometric distribution has no memory, for if the event of a failure has not occurred during the first s trials, then the probability that a failure will not occur in the next t trials is the same as the probability that it will not occur in the first t trials. In other words, the information that a failure has not occurred in the first s trials is “forgotten” in the subsequent calculations.)