please answer all 3

3. Suppose the time it takes a nine-year-old to eat a donut is between 1 and 4 minutes. Let X be the time, in minutes, it takes a nine-year-old to eat a donut and X-U(1,4). Find the probability function f(x), and the average/medium X over the support range. Find the probability that a different nine-year old child eats a donut in more than 2 minutes given that the child has already been eating the donut for more than 1.5 minutes. 4. Consider a used car market. There is a fraction of p lemons, a fraction of q lemons plus, and a fraction of 1-p-q peaches. Used car sellers value peaches at $200k, lemons plus at $150k and lemons at $100k. Used car buyers value peaches at $240k, lemons plus at $170k and lemons at $120k. The seller of the car knows the type of the cars and the potential buyer does not. What type of problem is this? Adverse selection or moral hazard? Why? Suppose p=0.2, q=0.4, what are the market equilibrium prices? What kinds of cars are traded in the equilibrium? What is the potential solution for this type of problem? 5. From the balance sheet below compute the debt to equity ratio and debt to capital ratio. Balance Sheet Assets Cash Accounts Receivable Inventory Property & Equipment Total Assets 167.971 5,100 7,805 45,500 226,376 3,902 50,000 53,902 Liabilities Accounts Payable Debt Total Liabilities Shareholder's Equity Equity Capital Retained Earnings Shareholder's Equity Total Liabilities & Shareholder's Equity 170,000 2,474 172,474 226,376