(a) Consider the set (1,..., n). We generate a subset X of this set as follows:...

Transcribed Image Text:

(a) Consider the set (1,..., n). We generate a subset X of this set as follows: a fair coin is flipped independently for each element of the set; if the coin lands heads then the element is added to X, and otherwise it is not. Argue that the resulting set X is equally likely to be any one of the 2" possible subsets. (b) Suppose that two sets X and Y are chosen independently and uniformly at random from all the 2n subsets of (1,..., n). Determine Pr(X≤ Y) and Pr(XU Y (1,..., n)). (Hint: Use the part (a) of this problem.) (a) Consider the set (1,..., n). We generate a subset X of this set as follows: a fair coin is flipped independently for each element of the set; if the coin lands heads then the element is added to X, and otherwise it is not. Argue that the resulting set X is equally likely to be any one of the 2" possible subsets. (b) Suppose that two sets X and Y are chosen independently and uniformly at random from all the 2n subsets of (1,..., n). Determine Pr(X≤ Y) and Pr(XU Y (1,..., n)). (Hint: Use the part (a) of this problem.)

Answer rating: 100% (QA)

a Since each element has a 50 chance of being added to X independent of the other elements and there ... View the full answer