Mike is a professional stuntman who performs dangerous

motorcycle jumps at extreme sports events around the world. The

annual cost of repairs to his motorcycle is modeled by a two

parameter Pareto distribution with

=

5000

and

=

2

. An

insurance reimburses

Mike's motorcycle repair costs subject to the

following provisions

1) Mike pays an annual ordinary deductible of 1000 each year.

2) Mike pays 20% of repair costs between 1000 and 6000 each

year.

3) Mike pays 100% of the annual repair costs above 6000 until

Mike has paid 10,000 out of pocket repair costs each year.

4) Mike pays 10% of the remaining repair costs each year.

Calculate the expe

cted annual insurance reimburse

ment.