2 A Loss Occurrence May Be Caused By Wind W Fire F Or Earthquake E Wind Fire And Earthquake Losses Occur Indep 1 (127.1 KiB) Viewed 26 times
2. A loss occurrence may be caused by Wind (W), Fire (F) or Earthquake (E). Wind, Fire and Earthquake losses occur independently of one another. Wind losses follow a Poisson Process. The expected amount of time between Wind losses is 10 years. Fire losses follow a Poisson Process. The expected amount of time between Fire a losses is 5 years. Earthquake losses follow a Poisson Process. The expected amount of time between Earthquake losses is 20 years. The size of Wind losses follows an Exponential Distribution with cumulative dis- tribution function (CDF) Fw(x) =1-e-0.002x, 002x, x > 0. The size of Fire losses follows a Pareto Distribution with CDF Ff(x) = 1- 2 2800)?, x 20. х = The size of Earthquake losses follows a Weibull Distribution with CDF FE(x) 1- e-(2006). ", r > 0.
(a) What is the probability of the first Earthquake loss occurring prior to a Wind loss? (4 marks] (b) What is the probability that the 3rd loss has occurred by time t = 8 years? [4 marks] (c) You observe the 5th loss by time t the 2nd loss occurred before time t 20 years. What is the probability that 10 years? (4 marks] = (d) What is the probability that there have been at least 2 wind losses, at least 2 fire losses and at least one earthquake loss by time t 20 years? [4 marks] (e) A loss of size greater than 2,000 is observed, what is the probability that the loss is a Wind loss? (9 marks)
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