The life cycle of an organism is controlled by shocks (e.g. virus attacks, accidents) in the following way: A healthy organism has an exponential lifetime L with parameter λ h . If a shock occurs, the...

The life cycle of an organism is controlled by shocks (e.g. virus attacks, accidents) in the following way: A healthy organism has an exponential lifetime L with parameter λ_h. If a shock occurs, the organism falls sick and, when being in this state, its (residual) lifetime S is exponential with parameter

However, a sick organism may recover and return to the healthy state. This occurs in an exponential time R with parameter If during a pe μ. riod of sickness another shock occurs, the organism cannot recover and will die a random time D after the occurrence of the second shock. is assu D med to be exponential with parameter

The random variables L, S, R, and D are assumed to be independent.

(1) Describe the evolvement in time of the states the organism may be in by a Markov chain.

(2) Determine the mean lifetime of the organism.