(3) A die is rolled 24 times. Let X be the number of fives in the first 16 rolls and let Y be the number of fives in all 24 rolls. Note that X follows Binom(16, 1/6) and Y follows Binom(24, 1/6). However, it is not clear whether X and Y are independent. (In fact, they are not independent.) (a) [1pt] Fill in the blank and explain your answer: "The values of x for which P(X = x, Y = 4) is positive range are 0, 1, ..., ." (b) [1pt] For the values of a in the range you found in (a), find P(X = x, Y = 4). (c) [1pt] For the values of x in the range you found in (a), find P(X = x |Y = 4). (d) [Ipt] Fill in the blanks. The first blank should be filled with the name of a famous distribution: "The conditional probabilities in (c) are the same as those in the distribution with parameters (e) [1pt] Suppose instead the problem had been that a coin is tossed 24 times; X is the number of heads in the first 16 tosses; Y is the number of heads in all 24 tosses; repeat parts (a)-(d) under these assumptions. Would your answer to part (d) have been different? Explain; you don't have to calculate and write out parts (a)-(d) for this new situation, but you can if you wish