An investor considers investing $$13,000$ in the stock market. He believes that the probability is $0\mathrm{.}24$ that the economy will improve, $0\mathrm{.}46$ that it will stay the same, and $0\mathrm{.}30$ that it will deteriorate. Further, if the economy improves, he expects his investment to grow to $$21,000,$ but it can also go down to $$7,000$ if the economy deteriorates. If the economy stays the same, his investment will stay at $$13,000.$

a$.$ What is the expected value of his investment?

Expected value

b$.$ What should the investor do if he is risk neutral?

Investor

invest the $$13,000.$

c$.$ Is the decision clear$-$cut if he is risk averse?

Yes

No

justify your answer