How do you prove that if X converges in probability and expectation that this implies convergence in mean? I think I have to use Chebyshev's Inequality, but am not sure how to incorporate the expectation convergence. Thanks
Convergence in expectation problem
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probability-theory
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4What is the difference between convergence in expectation and convergence in mean? – 2012-11-08
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0Xn--> X in l1 is convergence in mean, and E[Xn]--> E[X] is convergence in expectation. Sorry I don't know of a good way to type this in using Latex. – 2012-11-08
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0Beware that your terminology is somewhat non standard. Anyway, the result does not hold, see my answer. – 2012-11-09