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. √X₁ and Y = a/X; converge in prob- (a) Verify that the sequences defined by Y₁ ability. = (b) Use the results in part (a) to prove the fact used in Example 5.5.18, that σ/Sn converges in probability to 1.