(20 points) Prof. Lavieri is planning on buying a new car before the baby comes. She knows she wants to buy a GMC Terrain. Each month she must , or wait to see what next month's incentives are. If she buys the car, she will buy it at the dealers best price (which includes incentives). Otherwise, the following month there is a 20% chance the price will go up by $1,000, a 30% chance the price will go down by $1,000 and a 50% chance the price will not change. decide whether to buy a car Assume that the price will never go below $30,000 nor above S36,000. Also, assume the price is always a multiple of $1,000. If the price ever reaches $36,000, you know it will go down by $1,000 or stay the same with equal probabilities. If the price ever reaches $30,000, then it will never go up again. If Prof. Lavieri has not bought the car at the begining of November (she has 5 months to buy the car), she will have to buy it at month 6 at a different dealer (closer to her home) for S37,000. Formulate this problem as an MDP, clearly stating the decision epochs, states, actions, transition probabilities and rewards. (20 points) Prof. Lavieri is planning on buying a new car before the baby comes. She knows she wants to buy a GMC Terrain. Each month she must , or wait to see what next month's incentives are. If she buys the car, she will buy it at the dealers best price (which includes incentives). Otherwise, the following month there is a 20% chance the price will go up by $1,000, a 30% chance the price will go down by $1,000 and a 50% chance the price will not change. decide whether to buy a car Assume that the price will never go below $30,000 nor above S36,000. Also, assume the price is always a multiple of $1,000. If the price ever reaches $36,000, you know it will go down by $1,000 or stay the same with equal probabilities. If the price ever reaches $30,000, then it will never go up again. If Prof. Lavieri has not bought the car at the begining of November (she has 5 months to buy the car), she will have to buy it at month 6 at a different dealer (closer to her home) for S37,000. Formulate this problem as an MDP, clearly stating the decision epochs, states, actions, transition probabilities and rewards