Random Vector

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Definition

ProbabilityStochasticProcesses

Let $X_1,...,X_n$ be $n$ random variables. The vector $X=(X_1,..,X_n)^T$ is called a random vector. So we define $X:S\to\mathbb{R}^n$ such that $(S,p)$ is the underlying probability space.

A random vector $Z=(X_{1},\dots,X_{n})$ is a Borel function from $(\Omega,\mathcal{F},\mathbb{P})$ to $\mathbb{R}^{n}$ .

Linked from

Finite Variance = Autocorrelation symmetric + positive semidefinite

Kalman Filter

Static Quadratic Team

Bit Allocation Problem

Transform Coding with Scalar Quantization

High Resolution Optimality of KLT

Differential Entropy

Multivariate Gaussian

Joint Entropy

Mutual Information

Vector Quantizer

Covariance Matrix

Jensen's Inequality

Random Vector

Joint Distribution Function

Summary of MATH 895

Gaussian Process