Please show your work for each problem and bold/make clear the final answer. 1. Assume a firm owns a small warehouse. The warehouse is subject to the risk of a fire. Below is the probability distribution for losses: Loss ($) 0 3,750 8,250 9,500 11,000 P(Loss) 0.72 0.13 0.08 0.05 0.02 The firm has six current risk management options it can use to manage this risk: [1] Retention with a worry value of $650. [2] Insurance policy with a face amount (FA) of $13,000, a premium cost of $1,500 and a deductible of 180. Implement a loss reduction program that costs $50 and changes the probability of a $8,250 loss to 10%, a $9,500 loss to 4%, and a $11,000 loss to 1%. All other loss probabilities are kept the same. This option has a worry value of $425. [3] Insurance of $11,000 with a premium cost of $2,100. [4] Insurance policy with a FA of $11,000, a premium of $1,850, and a deductible of 200. This option has a worry value of $400. [5] Insurance policy with a face amount (FA) of $11,000, a premium cost of $1,650 and a deductible of 150. Implement a loss prevention program that costs $75 and changes the probability of a $0 loss to 73%, a $3,75 loss to 14%, a $9,500 loss to 4%, and a $11,000 loss to 1%. The loss of $8,250 stays at 8%. This option has a worry value of $450. [6] Insurance policy with a FA of $13,000, a premium of $1,700, and a deductible of 175. This option has a worry value of $415. a. Construct a loss matrix. What is the expected cost for each option? (3 points each) b. Assume that the risk manager makes decisions based on total cost. What option would she choose? (2 points)