This is a problem for Risk Management Class: Show your work in order to receive

This is a problem for Risk Management Class:
Show your work in order to receive credit for your submission.
A risk averse investor owns a $100,000 classic automobile. The automobile faces loss with the following probability distribution:
80% — No Loss
10% — $10,000 Loss
5% — $20,000 Loss
3% — $50,000 Loss
2% — 75,000 Loss
What is the expected value of the vehicle taking into consideration the possible losses? (2 points)
Calculate the investor’s certainty equivalent and risk premium for this vehicle if the investor’s utility function is defined as U(X)=X−−√. (2 points)
Calculate the investor’s certainty equivalent and risk premium for this vehicle if the investor’s utility function is defined as U(X)=ln(X). (2 points)
What is the difference in the risk premium between these two utility functions? Explain why the risk premium is difference from both a math perspective (i.e., the mathematical reason for the difference) and from an economic perspective (i.e., the economic rationale for the difference). (4 points)