# Questions tagged [random-vector]

The tag has no usage guidance.

26 questions
Filter by
Sorted by
Tagged with
Background. Let $V = (X,Y)$ be a random vector in 2-dimensions uniformly distributed over two disjoint regions $R_X \cup R_Y$ defined as follows: \begin{align} R_X &= ([0,1] \times [0,1]) \... 0answers 20 views ### What is the entropy of multivariate data multiplied by a vector? It is a general rule that for multivariate data \boldsymbol{X} and a matrix \boldsymbol{A}, their entropy ish(\boldsymbol{A} \boldsymbol{X}) = h(\boldsymbol{X}) + \ln |\det \boldsymbol{A}|$$(... 1answer 20 views ### Correlation between two vectors sharing some elements Suppose \mathbf{x,y} are column vectors of length n, where x_i,y_i \sim \mathcal{D}, \forall i \in \{1,2,\ldots ,n\}. \mathbf{z} shares m elements with \mathbf{x} and n-m elements with \... 2answers 32 views ### Are two random vectors independent if their corresponding components are all independent? Let \mathbf{X} = (X_1,\ldots,X_n) and \mathbf{Y} = (Y_1,\ldots,Y_n) be random vectors, and let f_{\mathbf{X}}(x_1,\ldots,x_n) and f_{\mathbf{Y}}(y_1,\ldots,y_n) be their respective pdfs or ... 0answers 18 views ### Published source for D-dimensional behaviour of Dot-Product I am currently studying the behaviour of the dot product between two random vectors in R^d. Specifically I wanted to start with the case of uniform random vectors on \mathcal{S}^{d-1}. I found ... 2answers 261 views ### Variance and asymptotic normality of \frac{1}{n-1}\sum_{i=1}^{n-1}(x_{i+1}-x_i)^2, where X \sim \mathcal{N}(0,1) Consider a length n vector \mathbf{x} containing n i.i.d. observations \{x_i\}_{i=1}^n of a standard normal random variable X. Let \mathbf{z} be a length n-1 vector whose entries are ... 0answers 8 views ### Correct way to present the definition a of Markov process of order p for a vector process? Usually when we define a Markov process of order p for a univariate time-series \{X_t\in\mathbb{R},t=1,2,\cdots\}, the definition is presented as follows \begin{equation} P(X_t\leq x_t\mid x_1,\... 0answers 18 views ### Distribution of the dot product between random unit vectors [duplicate] Let X,X' be two random vectors on the sphere S^{d-1}. What is the distribution of their dot product X\cdot X' in the following cases: X,X' independent with uniform distribution on the sphere ... 1answer 58 views ### Assume X,Y are two independent random variables. Let Z=f(X,Y). If Z is independent of X, f(X,Y) is constant in X. Is this true? Let X\in \mathbb{R}^n and Y\in \mathbb{R}^m be two independent random vectors. Then, say that we have a third real valued random variable Z=f(X,Y), with f being measurable. Say that we know ... 1answer 32 views ### Hypothesis Test on the Difference between two random vectors Each of my vectors consists of beta estimates for two separate models of the same data and the same number of explanatory variables. The question is asking whether the difference between these two ... 0answers 36 views ### How would you decorrelate a collection of vectors so that two vectors are uncorrelated? Suppose X_1, \ldots, X_K are all \mathbb{R}^d-dimensional random variables each with correlation matrix \text{Var}(X_k) = \Sigma_{k} \in \mathbb{R}^{d \times d}. Suppose we observe samples X_{... 1answer 33 views ### If cov(x_i,T_i)>0 can I show \mathbb{E}[\frac{T'x}{T'T}] > 0? x,T are vectors with cov(x_i,T_i)>0. Without specifying f(x,T), is it possible to determine the sign of \mathbb{E}[\frac{T'x}{T'T}]? 0answers 14 views ### I don't understand the task of finding the correlation in WordSimilarity-353 My issue is the following, I have created word embeddings using WordNet, and to test my embeddings to see how they stack up against the word similarities in WordSimilarity-353 I'm running a script ... 0answers 38 views ### Expected value of product of 2 correlated random vectors Let x and y be complex Gaussian random vectors with length L, and \mathbb{E}[x]=a and \mathbb{E}[y]=b, and they are correlated such that c = \mathbb{E}\left[\left|\mathbf{\mathit{\mathbf{x}}}^{T}... 0answers 155 views ### (Co)Variance of a random matrix The expected value \mathbb{E}[\mathbf{x}] of a random vector \mathbf{x} \in \mathbb{R}^{n \times 1} is the vector of the expected values of each individual random variable \mathbf{x} contains. ... 0answers 22 views ### probability density of a random vector greater than some value? [duplicate] In single dimension, the probability that a random variable X is greater than some value x is easily related to the cumulative distribution(c.d.f.) as Pr(X > x) = 1 - F(x) if only Pr[X \leq ... 0answers 36 views ### The joint distribution of Y=AX and Z=BX given a projection matrix A and residual maker matrix B, and a random vector X with known pdf? This question follows on from a previous question I asked which was answered. It turns out my question lacked some important details, which was revealed by the answer posted on that thread. This is ... 1answer 914 views ### Distribution of the L^{2} norm of a vector of components drawn from Gaussian distributions I recently asked this question involving uniform distributions. I am wondering what would be the equivalent for Gaussian distributions. The problem states as follows. We consider a random vector \... 1answer 229 views ### L_2 norm of product of two vectors Let's assume we have two matrices A^{d\times 1} and B^{1 \times e}, and we define their product as C^{d\times e}. Assuming A,B are real valued with all entries in [-1,1]. I can intuitively ... 1answer 28 views ### Test for equality of means for vector-valued random process with different variances I am studying linearity range of an RF amplifier (henceforth DUT). For that I am stimulating the DUT with a periodic deterministic probe signal (which is known only roughly) and measuring the DUT's ... 3answers 2k views ### Does mean centering reduce covariance? Assuming I have two non-independent random variables and I want to reduce covariance between them as much as possible without loosing too much "signal", does mean centering help? I read somewhere that ... 0answers 382 views ### Distribution of the L^2 norm of a vector of components drawn from uniform distributions We consider a random vector \vec{v} = \left(x_{1}, x_{2}, \dots, x_{n}\right) built from n real random variables drawn from a real continuous uniform distribution \mathcal{U\left(a, b\right)}, ... 1answer 86 views ### Covariance of sums of pairs of correlated variables Take two vectors of normally-distributed random variables \mathbf{x} = (x_1, x_2, \ldots x_n) \mathbf{y} = (y_1, y_2, \ldots y_n) where the covariance of each pair (x_i, y_i) is known, \... 2answers 160 views ### Suppose \mathbf{X, Y} are independent random vectors. Are their components independent? [duplicate] Let \mathbf{X} = (X_1, \dots, X_p)^\top and \mathbf{Y} = (Y_1, \dots, Y_p)^\top be independent. Does it then follow that X_i is independent with Y_j i.e. cov(X_i, Y_j) = 0? 1answer 87 views ### Conditional expectation of a vector Suppose we have two random vectors X=(X_1,X_2)^T and Y=(Y_1,\dots,Y_n)^T. I wish to find a simple definition or formula for$$ E_{X|Y=y}[X] $$Intuitively, I think the following is correct:$$ ...
I feel a little stupid asking this, but anyway: say I've got a random vector $a$ of size $p$ with covariance matrix ${\Sigma_a}$ of size $p\times p$, and another vector $b$ with its cov $\Sigma_b$. ...