Security A pays $ 100$100$ for sure at the end of the year and costs $95$95$ now. Security B has a uniform distribution of payout on the interval [80,120].$[80,120].$ Your utility function for wealth is U($($x)=−1/$)=-1/$x,$,$ and your initial wealth is $100.$100.$ You have no relevant consumption needs between now and the end of the year ($($i.$.$e.,$.,$ you are not limited in how much of your wealth you can invest).$).$ You can buy any real number of units of any security, i.$.$e.,$.,$ you are not limited to a whole number of

a)$)$ if the security A and B are the only investments available, what is the maximum price of security B at which you would be willing to buy?

b)$)$ Suppose there also exists security C,$,$ described by the same distribution as security B,$,$ and the payouts of the B and C are independent ($($and hence uncorrelated).$).$ What would now be the maximum prices of security B and C at which you would be willing to buy them?

c)$)$ now suppose that there are infinitely many security B1,$1,$ B2,$2,$ B3,.......,$3,.......,$ which all have the same distribution as security B.$.$ At what price would you buy them if they are all mutually independent?