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I need help undersanding convergence in distribution
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here is both the problem and the solution:

https://preview.redd.it/iyufcluo1rsc1.png?width=1566&format=png&auto=webp&s=9a4efd13f3bd1cc1e2ea74c6f68c8edbfd9ed815

I do not understand what this last line means, my definition of convergence in distribution is this:

https://preview.redd.it/i136b2pz1rsc1.png?width=542&format=png&auto=webp&s=cea2e37ce1b999e452dcbcfbf7239d739eb72850

Im confused because the limit as n goes to infinity for the cdf is zero, since y < infinity, and its impossible for something to be greater than infinity, but that means that the cdf of Yn at y =0 is the same thing as the cdf of yn as n goes to infinity so why are we saying there is no limiting distribution ?

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7 months ago