This Markov chain is used to predict the magnitude of the next volcanic eruption, based on the magnitude of the last one. It is estimated that in an eruption of level 1 a volume of 79m3 of lava is ejected, in an eruption of level 2 a volume of 316m3 of lava is ejected, and in an eruption of level 3 a volume of 1580m3 of lava is ejected.
(a) Estimate the average amount of lava thrown out during each eruption in a cycle of 300 consecutive eruptions.
(b) What is the expected number of eruptions between two eruptions of level 3?