(20 points) In class we defined Ds advantage in distinguishing between distributions X0,X1 as PrxX1[D(x)=1]PrxX0[D(x)=1]. 4 Now consider an alternative definition of advantage: 2Prb{0,1},xXb[D(x)=b]21. Here D is given a sample from a random choice of either X0 or X1, and tries to determine what the choice was. The advantage is double the amount by which D does better than random guessing (which would be correct with probability 1/2 ). Prove that the above two notions of advantage are equal (for the same D )