Problem 5. Remaining time: 105:43 (min:sec) (20 points) You are going to buy two tickets to the theater where the seats are given randomly by a computer algorithm. Unfortunately, the only avaible seats are 3 at the balcony, 3 at the mezzanine and 2 at the orchestra sections. Let X and Y represent, respectively, the number of balcony seats and mezzanine seats drawn for the tickets. Part A: basic calculations How many ways are there to select two places from the avaible seats at the theatre: Answer: Help for entering numbers List down the possible (x, y) pairs, seperated by commas: (x, y) pairs: Example: (1, 2), (3, 4), (5, 6), ... Help for entering lists Part B: joint distribution Calculate the values of the joint distribution, f(x, y) 0 1 2 o 2 Help for entering numbers Help for entering numbers Part C: marginal distributions List the values of the marjinal distributions, seperated by commas, hy) = Help for entering lists Part D: Probability Calculate the probability of having no seat(s) at the balcony in the condition of two seat(s) at mezzanine, P(x = ly Help for entering numbers