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Problem 5 (20 points) Two random variables are dened on repeated tossing of three fair coins: ' X is the number of heads obtained in each tossing of the three coins, ' Y is the absolute differeme between the numbers of heads and tails. For example, let H be head and T be tail, if the tossing result is HTI-I, X = 2, Y = 1; if the result is TTT, X = 0, Y = 3. (1) Specify the values of X and Y, respectively, for each possible outcome. TTT'ITHTHTTI-H-IHTTHTHHHTHHH X Y (2) In a table, list the joint probability mass function of (X, Y), as well as the marginal probability mass mctions of X and Y, respectively. (3) In a table, list the joint cumulative distribution function of (X, Y), as well as the marginal cumulative distribution functions of X and Y, respectively. (4) Are X and Y independent? Why? (5) Are X and Y correlated? Why