Between March 4 and 10, 1985, a volcanic complex has presented 19 episodes of volcanic activity with earthquakes associated with rock fracturing, which may or may not present surface activity. Then...

Extracted text: Between March 4 and 10, 1985, a volcanic complex has presented 19 episodes of volcanic activity with earthquakes associated with rock fracturing, which may or may not present surface activity. Then answer the following three questions: 1) Under the assumption that the episodes currently maintain the observed frequency and that they occur according to a Poisson process, what is the probability that the time elapsed between three episodes exceeds 13 hours? 2) So far 0.32% of the episodes present superficial activity. If this frequency remains constant, what is the probability, from now on, that surface activity will be observed for the 2nd time after the 10th seismic event? 3) So far the height reached by the column of material for each episode has a median equal to 800 meters with a coefficient of variation of 0.44%. Under the assumption that the height behaves as a Log-Normal random variable, what is the probability that the next column of material exceeds 1.19 kilometers?