TeXipedia

beta

Represents the second letter of the Greek alphabet, commonly used in mathematics, physics, and statistics as a variable or parameter.

Overview

A versatile Greek letter that appears extensively across scientific and mathematical notation:

  • Frequently used to denote angles in geometry and trigonometry
  • Common in statistical analysis to represent regression coefficients and type II error rates
  • Essential in physics for expressing various constants and ratios
  • Appears in engineering to denote gain factors and angular measurements
  • Used in finance and economics to measure systematic risk of investments

Examples

Representing a beta coefficient in linear regression.

y=β0+β1x+ϵy = \beta_0 + \beta_1 x + \epsilon 
y = \beta_0 + \beta_1 x + \epsilon

Showing beta decay in nuclear physics.

14C→14N+β−+νˉe^{14}\text{C} \rightarrow ^{14}\text{N} + \beta^- + \bar{\nu}_e 
^{14}\text{C} \rightarrow ^{14}\text{N} + \beta^- + \bar{\nu}_e

Expressing beta distribution parameters.

f(x;β1,β2)=xβ1−1(1−x)β2−1B(β1,β2)f(x; \beta_1, \beta_2) = \frac{x^{\beta_1-1}(1-x)^{\beta_2-1}}{B(\beta_1,\beta_2)} 
f(x; \beta_1, \beta_2) = \frac{x^{\beta_1-1}(1-x)^{\beta_2-1}}{B(\beta_1,\beta_2)}