LaTeX
\operatorname{Var}(X)=\mathbb E[X^2]-\mathbb E[X]^2Variables
- Define every symbol and unit before substitution.
- Check the domain, shape, and convention required by the formula.
How to use this formula
Expresses variance using first and second moments.
Important notes
- Verify assumptions and units before applying the expression.
- Keep exact values until the final rounding step when possible.
Quick example
Use the variance identity with a small known example, then verify the result independently.
Applicability, worked calculation, and verification
Assumptions and domain checks
- For the Variance Identity, verify assumptions and units before applying the expression.
- The event model, conditioning information, independence assumptions, and probability range must match the problem.
Worked example
Use the variance identity with a small known example, then verify the result independently.
Common mistakes
- Do not substitute sample and population quantities interchangeably in Variance Identity; map every symbol to its definition first.
- Do not assume events are independent or mutually exclusive unless the problem states or proves that condition.
Continue the workflow
Use Variance Identity in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\operatorname{Var}(X)=\mathbb E[X^2]-\mathbb E[X]^2. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Introductory Statistics 2eOpenStax, Rice University — Reviewed probability and statistics definitions, notation, and formulas.
Frequently asked questions
What is the Variance Identity used for?
Expresses variance using first and second moments.
Can I copy this formula as LaTeX?
Yes. Copy \operatorname{Var}(X)=\mathbb E[X^2]-\mathbb E[X]^2 or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.