Questions tagged [convergence-probability]

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MIT Statistic For Applications course Question 1

I'm having trouble understanding the answer to one of the mit opencourseware Statistic For Applications homeworks The question: (question 1.): [0] The answer: [1] The question asks to show this random ...
tom tom's user avatar
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1 vote
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Convergence of positive random vector

Suppose I have a sequence of positive random vectors $\vec{X}_N$ of fixed length $l$. That is, $\vec{X}_N = (x_N^{(1)}, x_N^{(2)},\cdots, x_N^{(l)})$ where each entry $x_N^{(i)} > 0$. Suppose I ...
random_passerby's user avatar
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Problem on convergence in distribution of a random vector

The issue is that I have to prove the following with limited resources. Problem: Let $X_n$ and $Y_n$ be p-dimensional random vectors. Show that if $X_n − Y_n \xrightarrow{P} 0$ and $X_n \xrightarrow{D}...
TryingHardToBecomeAGoodPrSlvr's user avatar
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limit of convergane in probability [closed]

I was learning about the convergence in probability. I'm unsure if looking at the epsiolon-delta definitions below which captures better the convergence in probability correctly. $$ \forall \epsilon,\...
Tomer Gigi's user avatar
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Universal concentration of random matrix

I am studying a family of random matrices and observe a universal concentration behavior which I would like to understand. Let $U$ be an $N \times N$ random unitary drawn from the Haar measure, and $Z ...
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