In a seismically active territory, earthquakes take place at an average rate of three per decade (one decade = 10 years) according to the Poisson process. Determine
(a) The probablity that the fourth earthquake after time t = 0 arrives within 2 years of the third earthquake.
(b) The probability that the fourth earthquake arrives by time t = 5 years.
(c) The probability that the elapsed time between the third earthquake to the tenth earthquake exceeds a decade?
(d) The expected time and variance until the arrival of the next eight earthquakes.