Technique 3: Pick two integers x and y independently and uniformly at random from I to M, inclusive. Let par be the probability that x and y are relatively prime. Then lim PM = 6 Let pi = 2, /2 = #, and py = be the probabilities of the desired events of Technique 1, Tech- nique 2, and Technique 3, respectively. For each technique, we apply each technique N times, then compute the proportion of the times each technique occurred, getting estimates pi, p2, and p3,, respectively. (a) For each , compute an expression X, in terms off, that would be an estimate of . (b) Using Chebyshev's Inequality, compute the minimum value of / such that X, is within & of n with 1 - 6 confidence. Your answer should be in terms of & and o. For Xi and X3, computing the minimum value of / will be more tricky, as the expressions for XI and Xy are not as nice as X2. (c) For i = 1 and 3, compute a constant c, such that X- ICE = IMI- PIL