Let X1, X2, ... be a sequence of random variables that converges in probability to a constant a. Assume that P(X, > 0) = 1 for all i. (a) Verify that the sequences defined by Y, = vX, and Y/ = a/X, converge in prob- ability. (b) Use the results in part (a) to prove the fact used in Example 5.5.18, that o/ Sn converges in probability to 1