／var／logmarcus chiu

Univariate Normal Distribution - Algebra

Created on · Last Modified on

given 2 independent random normal variables:

  • 𝑋 ~ 𝑁(𝑢𝑥, 𝜎𝑥2)
  • 𝑌 ~ 𝑁(𝑢𝑦, 𝜎𝑦2)

and constants:

  • 𝑎
  • 𝑏

then

  • 𝑎𝑋 ~ 𝑁(𝑎𝑢𝑥, 𝑎2𝜎𝑥2)
  • 𝑋 + 𝑏 ~ 𝑁(𝑢𝑥 + 𝑏, 𝜎𝑥2)
  • 𝑋 + 𝑌 ~ 𝑁(𝑢𝑥 + 𝑢𝑦, 𝜎𝑥2 + 𝜎𝑦2)
  • 𝑋 − 𝑌 ~ 𝑁(𝑢𝑥 − 𝑢𝑦, 𝜎𝑥2 + 𝜎𝑦2)