• 𝑑𝑉𝑎𝑟(𝑋) = 0 iff 𝑋 = 𝐄[𝑋] almost surely
• 𝑑𝑉𝑎𝑟(𝑋) = 0 iff every sample observation is identical
• 𝑑𝑉𝑎𝑟(𝐴 + 𝑏𝐶𝑋) = |𝑏| 𝑑𝑉𝑎𝑟(𝑋) for all:
  • constant vectors 𝐴
  • scalars 𝑏
  • orthonormal matrices 𝐶
• 𝑑𝑉𝑎𝑟(𝑋 + 𝑌) ≤ 𝑑𝑉𝑎𝑟(𝑋) + 𝑑𝑉𝑎𝑟(𝑌) if 𝑋 and 𝑌 are independent
• 𝑑𝑉𝑎𝑟(𝑋 + 𝑌) = 𝑑𝑉𝑎𝑟(𝑋) + 𝑑𝑉𝑎𝑟(𝑌) if 𝑋 and 𝑌 are independent, and if one of the random variables 𝑋 and 𝑌 is a constant