.. , . .: , ] In this exercise we'll calculate an expected payoff for purchasing a home in Miami, FL, using some (somewhat unrealistic) assumptions. Suppose you are considering purchasing a home 1n the Miami area; the current market value of the home is $300,000. You plan to keep the home for 20 years. What is the expected home value of the home 20 years from now? Suppose we have the following possible scenarios with estimated probabilities: Optimistic outcome (20% chance): Home values will rise 3% per year (80% increase in value over 20 years). 0 Middle outcome (25% chance): Home value will rise 1% per year (22% increase in value over 20 years) 0 Pessimistic outcome: (30% chance): Due to increasing risks from sea level rise home values decline by 40%. 0 Natural Disaster: (15% chance): Home is destroyed by natural disaster; insurance pays 75% of original market value. 0 Market Collapse (10% chance): Home value plummets to 20% of original market value after natural disaster strikes nearby neighborhoods. Let X be the home value in 20 years. Use the table below to calculate the expected value E(X). Event X Probability Contribution Optimistic $540,000 20% $108,000 Middle Pessimistic Natural Disaster Market Collapse