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Unformatted text preview: ACTSC 432  Loss Models 2 TEST #2 1. (15 marks) For a particular line of insurance business, it is believed that 60% of the risks are standard (with risk parameter & = & 1 ) and 40% are substandard (with risk parameter & = & 2 ). Given that the conditional distribution of the claim amount for these two types of risk are Pr ( X j = 5 j & = & 1 ) = 0 : 2 Pr ( X j = 5 j & = & 2 ) = 0 : 1 Pr ( X j = 10 j & = & 1 ) = 0 : 5 Pr ( X j = 10 j & = & 2 ) = 0 : 3 Pr ( X j = 20 j & = & 1 ) = 0 : 3 Pr ( X j = 20 j & = & 2 ) = 0 : 6 , and that the r.v.&s X 1 ; X 2 ; ::: are independent conditional on the risk parameter & , (a) ( 2 marks ) determine the hypothetical means for both types of risk Solution : ( & 1 ) = E [ X j j & = & 1 ] = (5) (0 : 2) + (10) (0 : 5) + (20) (0 : 3) = 12 , and ( & 2 ) = E [ X j j & = & 2 ] = (5) (0 : 1) + (10) (0 : 3) + (20) (0 : 6) = 15 : 5 . (b) ( 2 marks ) nd the process variance for both types of risk Solution: v ( & 1 ) = V ar ( X j j & = & 1 ) = E & X 2 j j & = &...
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This note was uploaded on 02/02/2010 for the course ACTSC 432 taught by Professor Davidlandriault during the Spring '09 term at Waterloo.
 Spring '09
 davidlandriault

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