Consider the Poisson process earthquake occurrences in Sec. 6.3.1.
(a) Is the probability of an occurrence in the next t years zero if no occurrences have been observed in the past t0 years? Assume a diffuse prior on λ. Compare to a forecast using the maximum-likelihood point estimate of λ.
(b) An earthquake of intensity MM (modified Mercalli) IX can be expected to disrupt a particular irrigation system (slides and fracture of canals). Intensities up to VIII have been recorded in the vicinity, but none of MM IX has been included in the record for the past 150 years. If each IX occurrence involves a random amount of damage with an expected value of $100,000, using the results above, what is the expected cost from earthquakes of intensity IX in the next 20 years? Assume that the system is fully repaired between earthquakes and that the amount of damage given an earthquake is independent of such repairs. (See, also, Cornell [1969].)