Please show steps

Suppose X is the random variable that represents the rate, and P(X) is the probability distribution function (PDF). We have: \fThe entrepreneur will pay a rate of X + 0.02 if borrows from Bank. The cost of borrowing will be BCB = (X + 0.02) =I= 500 if needs to borrow $500. The entrepreneur can also borrow from his personal credit at rate of 0.03 72, so the cost of borrowing will be BCC = 0.0372 * 500. He has to choose between certain rate of 0.0372 or uncertain rate of X + 0.02 Suppose he receives utility from net wealth from loan and the utility function is U(Wk), where Wk = 500 - BCk and k E {B, C}, where B is the Bank loan and C is the personal credit loan. . What would his wealth be if borrows from personal credit? Write the formula and do the calculation. . What would his wealth be if borrows from Bank? Show all the steps to nd out E[WB] = E [500 (X + 0.02) a: 500] \f5. Suppose the variance of the random variable X is risk. The personal credit loan has no risk, so the variance of WC is zero. The bank loan has risk. Find out the formula and do the calculation of the variance of WB