Consider the sequence of binary random variables {Kn};1 satisfying the following properties (a) X" e {0, b} for all n, where b is some positive real number, (b) for any xed a) E 9., the deterministic sequence {Xn(w)} has the property that for any integer k 2 0: 2 X2k+j(a)) = b. j=0 Thus, for any xed a), there is precisely one index nk within the interval Ik 2 {2", 2" + l,- -- ,2"'Jr1 1} such that Xnk(0)) = b. It follows that Xm(a)) = 0 for all m E Ik, m 7E nk. In addition, you are given that the index nk is equally likely to be any of the 2" indices within the interval 1k. (a) Identify the values of b (if any) for which this sequence converges to the zero RV in probability, (b) Identify the values of b (if any) for which this sequence converges in the mean square to the zero RV, (c) Identify the values of b (if any) for which this sequence converges almost surely to the zero RV. Explain fully, your answers