Question: Convergence in probability versus convergence in distribution. Let X and .Xn/n1 be real-valued random variables on the same probability space. Show the following: (a) Xn

Convergence in probability versus convergence in distribution. Let X and .Xn/n1 be real-valued random variables on the same probability space. Show the following:

(a) Xn !P X implies Xn !d X.

(b) The converse of

(a) does not hold in general, but it does when X is almost surely constant.

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