Question: 4. Let X1, X2,... be a sequence of random variables that converge in probability to a constant a. Assume that P(X > 0) =

4. Let X1, X2,... be a sequence of random variables that converge

4. Let X1, X2,... be a sequence of random variables that converge in probability to a constant a. Assume that P(X > 0) = 1 for all n. Show that sequences Y = x and Z = a/X, converge in probability. 5. Prove that a sequence of random variables X1, X2,... converges in probability to a constant if and only if it also converges in distribution to .

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