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Questions tagged [convergence-distribution]

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Almost Sure Convergence of Rayleigh Distributed Random Variables

I am working on a problem involving almost sure convergence and Rayleigh distributed random variables, and I need some help to confirm my understanding and approach. The problem is as follows: Let $...
bruno's user avatar
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Central limit theorem: negative moments

Let $X_{1},\ldots,X_{N}$ be i.i.d. random variables with mean 0 and variance 1. Assume that $X_{i}$ are continuous random variables with all finite moments and a nice density function. Let \begin{...
Ele'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