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| *Loan,banking and credit>>>insurance claims |
Under an insurance policy a maximum of 5 claims may be filed per year by a policy holder. Let p^n be the p th |
Under an insurance policy a maximum of 5 claims may be filed per year by a policy holder. Let p^n be the p that a policy holder files n claims during the given year, where n = 1, 2, 3, 4, 5. An actuary makes the following observations: i) p^n 鈮?p^n + 1 for n = 1, 2, 3, 4. ii) The difference between p^n and p^n+1 is the same for n = 0, 1, 2, 3, 4. iii) Exactly 40% of policy holders file fewer than 2 claims during the given year. Calculate the probability that a random policy holder will file more than 3 claims during the given year. P(0)-P(1)=P(1)-P(2)=...=P(4)-P... Let P(0)-P(1)=P(1)-P(2)=...=P(4)-P... = x P(0) + P(1) =0.4 2*P(0)-x=0.4 P(0)+P(1)+...+P(5)=1 6*P(0)-15x =1 24*P(0)=5 P(0)=5/24=25/120 x=1/60 P(4)+P(5)=2*P(0)-9*x =2*25/120-9/60 =32/120=4/15 |
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