Unformatted text preview: 120; if X > 160, the policy pays 70. Thus, the per loss random variable for the policy, denoted by Y L , is Y L = , X ≤ 80; X80 , 80 < X ≤ 120; 40 + 0 . 75( X120) , 120 < X ≤ 160; 70 , X > 160 . Let Y P be the per payment random variable for the policy. Then Y P = Y L  X > 80. (a) Determine F Y L ( y ), the cdf of Y L , for all y ∈ (∞ , ∞ ). [10 marks] (b) Determine F Y P ( y ), the cdf of Y P , for all y ∈ (∞ , ∞ ). [10 marks] (c) Calculate the probability of Pr { 40 ≤ Y L ≤ 50 } . [5 marks] (d) Calculate the probability of Pr { 30 ≤ Y P < 70 } . [5 marks] (e) Calculate the mean of the per loss of the policy. [5 marks] (f) Determine the median of the per payment of the policy. [5 marks] (g) Determine the 90th percentile of the per payment of the policy. [5 marks] [Total: 75 marks] 1...
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 Fall '09
 david
 Probability theory, insurance policy, 75%, total loss

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