Let X1, X2, ... be a sequence of random variables that converges in probability to a constant a

Name: Let X1, X2, ... be a sequence of random variables that converges in probability to a constant a > 0. Assume that P(Xi > 0) = 1 for all i. Show that the sequence defined by Yi = a/Xi converge in probability to 1 as i -> infinity.
Uploaded: 2022-06-09T16:54:58-08:00
Duration: 4 min 24 s
Channel: Minh Le
Description: Let X1, X2, ... be a sequence of random variables that converges in probability to a constant a > 0. Assume that P(Xi > 0) = 1 for all i. Show that the sequence defined by Yi = a/Xi converge in probability to 1 as i -> infinity.

Question

Minh Le · Accepted Answer

Step 1: Start with the definition of convergence in probability. We want to show that (Y_i = f

Question

Let X1, X2, ... be a sequence of random variables that converges in probability to a constant a > 0. Assume that P(Xi > 0) = 1 for all i. Show that the sequence defined by Yi = a/Xi converge in probability to 1 as i -> infinity.

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