Let X₁, X₂,... be a sequence of random variables that converges in probability to a constant a. Assume that P(X; > 0) =

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Let X X Be A Sequence Of Random Variables That Converges In Probability To A Constant A Assume That P X 0 1 (250.11 KiB) Viewed 12 times

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 Y₁ = ability. √X₁ and Y = a/X₁ converge in prob- √X; and Y (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.