The table below shows the probability distribution of a lottery prize X in dollars ($) with Pr(X = x) denoting the probability that the prize is a specific amount $x. X Pr(X = x) -10 0.50 0 0.25 10 0.20 50 100 0.02 TOTAL 1 You may use Excel for calculation in answering the questions below. Provide your numerical answers after rounding them to 2 digits after the decimal point. (Round up if the third digit is 5 or larger, down if it is 4 or smaller, e.g. type 1.78 if your calculation results in 1.783, type 0.04 if it results in 0.038, type 0.10 if it results in 0.101, etc.) However, in order to obtain accurate final answers, do not round numbers during your calculation. . Compute and type the missing probability, Pr(X = 50), in the space provided in the table. . The expected value of the prize, E(X), is equal to S . The standard deviation is a measure of absolute risk. For this lottery, it is equal to S Consider another lottery prize Y that is equal to Y = - 0.1 + 0.8X where X is the prize that we considered above. . The expected value of the prize, E(Y), is equal to S . The standard deviation of Y is equal to S Based on your comparison of the coefficients of variation for X and Y, which lottery is preferred