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I have exam tomorrow will you help me to solve this problem

  1. Given $Y_n$ are random variables with characteristic function $T_n$, show they are weakly converging to zero iff there is a $\delta>0$ so that $T_n(t)\to1$ for $|t|<\delta$.
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    It's not clear what's to be shown; you'll need to write it slightly more carefully.2011-04-26
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    show that if Yn are random variable with characteristic funtion Tn which weakly convering to zero iff there is a delta>zero so that Tn(t)-->1 for mod t2011-04-26
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    Is there supposed to be another question after that? Because you labelled the question with "1" and I didn't want to change that. However, if there is no other question, it looks a bit silly.2011-04-26
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    This is a consequence of the continuity theorem for characteristic functions, so I assume you may not use that in your proof. What can you use?2011-04-26

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