2. You own two different apartment buildings in the city of Philadelphia. The rst building is located in North Philadelphia near the campus of Temple University. The second building is located in West Philadelphia near the campus of Drexel University. You are analyzing re statistics. For the exercise only one of two outcomes can occur a fire or no re. The odds of a tire occurring at the North Philadelphia building is 12% and the odds of a fire occurring at the West Philadelphia building is 20%. a. What is the probability the North Philadelphia building will not have a re? (1 point) b. What is the probability both buildings will have a re? (1 point) c. What is the probability that neither building will have a fire? (1 point) 3. You have been hired by Ajax Corporation in 2023 to complete two different shipping contracts. Ifyou are late with the delivery. there are penalties. The rst contract involves delivering 3 vehicles to California. You have a 25% probability of being late which would result in a $9.000 penalty. The second contract is delivering a large refrigerator to Florida. You have a 45% chance of being late which would result in a $3,000 penalty. If either delivery is on time a penalty will not be charged. a. What is the expected cost (penalty) of the projects that you are doing for Ajax in 2023? (5 points) 4. Assume that United Delivery Service (UDP), a mail service company, has distribution centers all along the East coast. UDP uses a eet of 500 delivery trucks in its operations dispersed among the various distribution centers. From past information the Chief Risk Ofcer for UDP has second contract is delivering a large refrigerator to Florida. You have a 45% chance of being late - which would result in a $3,000 penalty. If either delivery is on time - a penalty will not be charged. a. What is the expected cost (penalty) of the projects that you are doing for Ajax in 2023? (5 points) 4. Assume that United Delivery Service (UDP), a mail service company, has distribution centers all along the East coast. UDP uses a fleet of 500 delivery trucks in its operations dispersed among the various distribution centers. From past information the Chief Risk Officer for UDP has constructed the following probability distribution for the number of losses per truck per month. # of losses per truck per month Probability 0 0.03 0.20 2 0.30 0.32 UI A W 0.12 0.03 2# of losses per truck per month \\ 0 Probability 0.03 0.20 0.30 0.32 0.12 a. Calculate expected value of frequency per truck per month. (3 5. UDP has one major competitor on the East Coast, Speedy Delivery (SD). SD has similar operations and services as does UDP. SD has a smaller also has a eet of 500 trucks. From past information SD has collected the following data for the number of losses per truck per month. # of trucks having these # of losses per truck per month losses a. As a new hire in SD's risk management department, you are asked to derive the probability distribution for frequency based on the information provided above. (3 points) b. Calculate expected value of frequency per truck per month. (2 points) 0. Now you are looking at the data from UDP and SD. You would like to know which company faces the most risk in regard to the frequency calculation? You must prove it statistically just guessing the correct one will not be marked correct (8 points) From past information, SD has constructed the following distribution related to dollar amount of losses when accidents do occur. b. Calculate expected value of frequency per truck per month. (2 points) 0. Now you are looking at the data from UDP and SD. You would like to know which company faces the most risk in regard to the frequency calculation? You must prove it statistically just guessing the correct one will not be marked correct (8 points) From past information, SD has constructed the following distribution related to dollar amount of losses when accidents do occur. Probability of dollar $ amount of losses loss l 200 0.40 l 500 0.30 l 1500 0.25 l 3000 0.05 d. Calculate the expected value of severity for SD. (3 points) e. Calculate the expected loss per truck per month for SD. (3 points)