Consider the sequence of binary random variables satisfying the following properties

Consider the sequence of binary random variables * *~ | ~_` _ I satisfying the following properties (a) {` E |O, 61 for all A, where b is some positive real number , ibj for any fixed WEIL , the deterministic sequence ( {, I'w']] has the property that for any integer *_ O : [ X` ; ( 0 ) = 6 , i.e., there is precisely one nonzero element of the sequence {{, I'w'!) that takes on the value & within the* interval | 2", 2* + 1 . ... 2471 _ I' for any &_ O and all ?" possibilities are equally likely . ( a) Identify the values of' 6 ( if any ; for which this sequence converges in probability* I bj Identify the values of' 6 (if any ; for which this sequence converges in the mean square . ( C ) Identify the values of ! ( if any ; for which this sequence converges almost surely ! Explain fully, Your answers