A company insures airplanes. They crash at a rate of 0.16 crashes per month. Each crash costs $ Lognormal (150, 45) million.

a) What is the distribution (in a diagram format) of cost to the company for the next 5 years?

b) What is the distribution (in a diagram format) of the value of the liability if the company discounts it at the risk-free rate of 4%? Assume the time distribution for accident occurrence following the exponential distribution.

c) What pieces of information can be extracted from these diagrams? (Perform further analysis if required).