Question: An earthquake of magnitude M releases energy X such that M = log X. for earth quakes of magnitude greater that 3, suppose that M -3 has an exponential distribution with mean 2.
a) Find E(M) and Vαr (M) for an earthquake of magnitude greater than 3.
b) For an earthquake as in part a), find the density of X.
c) Consider two earthquakes, both of magnitude greater than 3, what is the probability that th e magnitude of the smaller earthquake is greater than 4? Assume that the magnitudes of the tow earthquakes are independent of each other.