(a) Suppose that a bank is considering issuing a risky loan in the amount of 88,000,000 dollars. Their analysts estimate that there is a 87% chance that it will be repaid in full at the end of the period, along with additional 12% of the principal (original amount) in interest. There is, furthermore, a 7% chance that only 83% of the principal (original value of the loan) will be returned, and a 6% chance of getting back nothing. Alternatively, the bank can put their money into state bonds, getting the principal back along with a modest interest of 2% lie, get back 89,760.000 dollars) with certainty. The risky loan is only worthwhile if the expected value of the amount that the bank will be repaid is higher than it would get back from the treasury bonds. Calculate the following: (i) The probability distribution of the amounts the bank will be repaid for the risky loan, as: . - a vector of the possible amounts of repayment. m a vector of their respective probabilities. (ii) _ The expected value of the amount of repayment. (iii) m The (population) standard deviation of the amount of repayment. (iv) u Based on the expected value, is the risky loan worth the risk? {TRUE or FALSE)