(35B 515] Assignment 5 1. Open the Excel file GSB 519 Additional Years of Life for Males. The random variable x =5, 1.5, 2.5,. . ...,11{}.5, where x denotes additional years of life beyond age zero. The second column shows the pmhahility that each specific value of it occurs. This column contains the probability mass values, x). For example, the probability that a new-bom male baby will live 25-5 years [not less or not more) is .D0133349, i.e., 3125.5) = . 133349. Find the following properties of the random variable x. a. mean h. median c. mode d. variance e. standard deviation f. skewness g. kurtosis h. coefficient of variation i. Find the value of the distribution function F{x) when x = 65.5- j. How much total probability is contained within two standard deviations of the mean? [You should use Excel in order to avoid hand calculations. However, do not use Excel commands like AVERAGE or STDEV; you will get incorrect answers if you do.] 2 [a] Consider the St. Petersburg Paradox problem first discussed by Daniel Bernoulli in HEB. The game consists of tossing a coin. The player gets a payoff of 2" where n is the number of times the coin is tossed to get the first head. So, if the sequence of tosses 1 yields TTTH, you get a payoff of 2" ; this payoff occurs with probability T . Compute the expected value of playing this game. (b) Assume that utility U is a function of wealth X given by U = X5 and that X = $1,D,t}l}. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 2'\" and the game is over. What is the expected payout of this game? 1F.t'tf'hat is the most you would pay to play the game if you require that your expected utility after playing the game must be equal to your utility before playing the game? Use the Goal Seek function {found in Data, What-If Analysis] in Excel and show your Excel work in the detailed part of your submission