Mr. Smith and Mr. Taylor are traveling on the Queen Mary ocean-liner from Southampton to New York City. They are carrying their entire belongings with them: $10,000 of sterling pounds each. There is one chance in ten that each man's money will get stolen during the trip.

A. Use a lottery to represent Mr. Smith and Mr. Taylor's current economic situation.

B. What is Mr. Smith's expected wealth? What is the statistical variance of his wealth?

The Cunard Line sailing company offers to fully insure each gentleman's wealth for a premium of $150. The two men have utility from income/wealth represented by the function U(W) = W^0.5.

C. Are Mr. Smith or Mr. Taylor being offered "fair insurance"? Explain.

D. Will Mr. Smith or Mr. Taylor buy the insurance? Show your work.

Mr. Rich is also traveling on the steamer carrying 10,000 sterling pounds. His utility from income/wealth is also represented by the function U(W) = W^0.5. However, being Mr. Rich, a very rich man, the 10,000 pounds he carries are just a small fraction of his total wealth.

E. Is Mr. Rich more or less likely than Mr. Smith and Mr. Taylor to buy the insurance policy offered by the Cunard Line?

Upon boarding the ocean liner, Mr. Smith offers Mr. Taylor to equally split any loss from theft. If neither man is robbed each still has his full 10,000 pounds. If one man is robbed, each man is left with 5,000 pounds, and if both men get robbed, they both lose all their money.

F. Do you think Mr. Taylor accepts the offer? Why?

[please answer all parts and explain all steps clearly so i can understand // learn :)]