Exercise 6.47 discussed the record losing streak of the Pittsburgh Pirates. In particular, if the Pirates’ chance of winning any single game is 0.42, then at
the beginning of a new season, the probability of them winning at least 81 games, and hence not adding another losing season to the streak, is about 0.024. The previous exercise mentions a type of random variable called the geometric random variable. A simple formula exists for calculating the mean of a geometric variable; if the probability of success on any given trial is p, then the expected number of trials required for the first success to occur is 1/p. If the first such trial is taken to be the 2000 Major League Baseball season (i.e., 5 years into their losing streak), during what year would we expect the Pirates to break their streak?