this is a game between randy and kathy. George is a dummy player, he receives no payoff. George wrote on a sheet of a paper one of the following integers: 1,2,3,4,5,6,7,8,9. No one else knows the number he wrote. Randy and kathy were each othr then asked to pick one integer from the list above, and the person whose number is closest to the number george wrote wins $1000 and other player wins $10. randy chose first. randy chose 7. hearing randy's choice, kathy who was barred from choosing the same number as randy, then chose 3. George then announced that he chose 9, so randy won $1000, kathy won $10. using the concept of expecetd value, analyze the choices of randy and kathy - did each of them choose wisely? if not, using expected values, determine how s/he should have played. is there a first-mover advantage? how do you know? a good strategy is for you to give a lot of thought to the situation before completing your work. show all calculations and carefully explain what you are doing. when doing your analysis, assume george chose his number randomly and, if there is a tie between randy and kathy as to whose chosen number is closest to george's number, assume a fair coin is flipped to see who between randy and kathy wins the $1000. show all of your work. a. given that randy chose 7, calculate the expected value to kathy from choosing 3. b. given that randy chose 7, what number should have kathy chosen? calculate the expected values for randy and kathy defending your answer. c. given that george chose randomly, what numbers should randy and kathy have chosen? calculate the appropriate expected values for randy and kathy defending your answer.