Somebody chooses two nonnegative integers X and Y and secretly writes them on two sheets of paper.

Somebody chooses two nonnegative integers X and Y and secretly writes them ontwo sheets of paper. The distrubution of (X, Y ) is unknown to you, but you do know that X and Y are different with probability 1. You choose one of the sheets at random, and observe the number on it. Call this random number W and the other number, still unknown to you, Z.Your task is to guess whether W is bigger than Z or not. You have access to a random numbergenerator, i.e., you can generate independent uniform (on [0, 1]) random variables at will, soyour strategy could be random.Exhibit a stategy for which the probability of being correct is 1/2 + , for some > 0. This may depend on the distribution of (X, Y ), but your strategy of course can not