Security A pays $ 100 for sure at the end of the year and costs $95 now. Security B has a uniform distribution of payout on the interval [80,120]. Your utility function for wealth is
U(x)=-1/x, and your initial wealth is $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 units.

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, B2, B3, ……, which all have the same distribution as security B. At what price would you buy them if they are all mutually independent? Why if they are all positively correlated, and the coefficient of correlation between any two of them is 0.2?