4. A company provides insurance to an arena for losses due to power failure: (i) The number of power failures in a year follows a Poisson distribution with mean 1. (ii) The distribution of ground-up losses per power failure is: a loss of 10,000 with probability 0.3; a loss of 20,000 with probability 0.3; and a loss of 50,000 with probability 0.4. (iii) The number of power failures and the amounts of losses are mutually independent. (iv) There is an annual deductible of 30,000. Calculate the expected amount of claims paid by the insurer in one year. 4. A company provides insurance to an arena for losses due to power failure: (i) The number of power failures in a year follows a Poisson distribution with mean 1. (ii) The distribution of ground-up losses per power failure is: a loss of 10,000 with probability 0.3; a loss of 20,000 with probability 0.3; and a loss of 50,000 with probability 0.4. (iii) The number of power failures and the amounts of losses are mutually independent. (iv) There is an annual deductible of 30,000. Calculate the expected amount of claims paid by the insurer in one year