3. Let's generalize our gambling example. Suppose that I have a $100 ticket that will pay a profit of P if team 1 wins. Moreover, suppose that the current odds for team 2 winning are P2:1. (a) (5 points) Find the amount x I should bet on team 2 to hedge my bet. (b) (7 points) Find my expected profit E in this case. Show that E is an increasing function of P2, bounded between the winning and losing sides of the $100 bet. Interpret the limits that P2 +0 and P2 +00. (c) (4 points) Under what conditions will your expected profit will be 0? Explain your answer in terms of your bet x. (d) (2 points) Use your formulas to verify the example given in class. 3. Let's generalize our gambling example. Suppose that I have a $100 ticket that will pay a profit of P if team 1 wins. Moreover, suppose that the current odds for team 2 winning are P2:1. (a) (5 points) Find the amount x I should bet on team 2 to hedge my bet. (b) (7 points) Find my expected profit E in this case. Show that E is an increasing function of P2, bounded between the winning and losing sides of the $100 bet. Interpret the limits that P2 +0 and P2 +00. (c) (4 points) Under what conditions will your expected profit will be 0? Explain your answer in terms of your bet x. (d) (2 points) Use your formulas to verify the example given in class