Samuelson Co. is a cars manufacturer for exports. The size of export has been stable in recent years and is expected to stay at the same level in the foreseeable future. In the last 5 years, Samuelson Co. had been sued by foreign consumers for product defects once every quarter. All of the lawsuits were settled out of- court. The table below presents the size of the settlement and the corresponding number of lawsuits.

Year	2013	2014	2015	2016	2018
Size of Settlement (US$ millions)	$10	$1	$9	$6	$7
Number of Lawsuits	1	5	3	6	5

Samuelson Co. is considering the use of liability insurance from Nopay Insurance and self-insurance against future losses due to lawsuits. Samuelson Co.'s risk manager believes that the size of quarterly settlement will follow the same distribution as in the last 5 years.

(a) Suppose Samuelson Co. wants to buy liability insurance from Nopay Insurance to protect against quarterly expected loss. What should be the fair quarterly premium?

(b) Suppose Samuelson Co. figures that it can comfortably handle quarterly liability loss up to the expected loss level. On top of that, Samuelson Co. is considering setting up a risk fund that will protect Samuelson Co. 80% of the time. Determine the size of the risk fund.

(c) Suppose Samuelson Co. also considers buying liability insurance to protect against extreme loss that will wipe out the entire risk fund in (b).

(d) Determine the fair premium for protection against extreme loss.