Answer the following questions

Claims on a portfolio of policies occur according to a Poisson process with a mean rate of 5 claims per day. Claim amounts are 10, 20 or 30. 20% of claims are of amount 10, 70% are of amount 20 and 10% are of amount 30. (i) Calculate the expected waiting time until the first claim of amount 30. [1] (ii) Calculate the probability that there are at least 10 claims during the first 2 days, given that there were exactly 6 claims during the first day. [2] (iii) Calculate the probability that there are at least 2 claims of amount 20 during the first day and at least 3 claims of amount 20 during the first 2 days. [3] (iv) Calculate the conditional variance of the number of claims during the first day, given that there are 2 claims of amount 10 during the first day. [3] [Total 9]You are deciding how to spend next Saturday afternoon. You have four mutually exclusive choices, which will give you the following units of pleasure: 1. driving in a car rally + 70 2. playing squash + 40 3. watching television + 25 4. going shopping + 15 (i) What is the opportunity cost of driving in a car rally? (ii) What is the opportunity cost of going shopping