TeXipedia

xi

Represents a lowercase Greek letter commonly used as a variable or parameter in mathematics and physics.

Overview

Serves as a versatile mathematical symbol frequently encountered in academic writing and scientific notation.

  • Often used to denote unknown variables in equations and mathematical proofs
  • Common in statistical analysis for representing random variables
  • Appears regularly in physics equations, particularly in quantum mechanics
  • Frequently employed in engineering contexts for dimensionless parameters
  • Part of the standard Greek alphabet notation used throughout scientific literature

Examples

Using xi as a variable in a probability density function.

fξ(x)=12πe−x22f_{\xi}(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}} 
f_{\xi}(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}}

Representing an arbitrary eigenvalue in linear algebra.

Av=ξvA\mathbf{v} = \xi\mathbf{v} 
A\mathbf{v} = \xi\mathbf{v}

Denoting a random variable in statistics.

P(ξ>x)=∫x∞fξ(t) dtP(\xi > x) = \int_x^\infty f_{\xi}(t)\,dt 
P(\xi > x) = \int_x^\infty f_{\xi}(t)\,dt