Gaussian Random Variable

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Gaussian Random Variable

Definition (Gaussian)

A continuous RV $X$ with pdf $f(x)=\frac{1}{\sqrt{2\pi\sigma^{2}}}e^{\frac{-(x-\mu)^{2}}{2\sigma^{2}}}$ is called a normal RV with mean $\mu$ and variance $\sigma^{2}$ . For RV $X\sim N(\mu,\sigma^2)$ $\begin{align*} E[X]&=\mu\\ \mathrm{Var}(X)&=\sigma^{2} \end{align*}$

Linked from

Kalman Filter

LQG Teams

High Resolution Optimality of KLT

Differential Entropy

Discrete-Time Memoryless Gaussian Channel (AWGN Channel)

Estimation Error and differential entropy

Gaussian Noise Minimizes Capacity of Additive-Noise Channel

Upper Bound on Channel Capacity

Multivariate Gaussian

Standard Normal Random Variable

Brownian Motion

Log-Sum-Exp Trick

Continuous-time Gaussian process motion planning via probabilistic inference

Radial Basis Function