LaTeX
P(X=k)=(1-p)^{k-1}pVariables
- p: success probability
- k: positive trial number
How to use this formula
Models the trial number of the first success.
Important notes
- This convention starts counting at k=1.
Quick example
P(X=1)=p.
Applicability, worked calculation, and verification
Assumptions and domain checks
- This convention starts counting at k=1.
- The event model, conditioning information, independence assumptions, and probability range must match the problem.
Worked example
P(X=1)=p.
Common mistakes
- Do not substitute sample and population quantities interchangeably in Geometric Distribution PMF; 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 Geometric Distribution PMF 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
P(X=k)=(1-p)^{k-1}p. - 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 Geometric Distribution PMF used for?
Models the trial number of the first success.
Can I copy this formula as LaTeX?
Yes. Copy P(X=k)=(1-p)^{k-1}p 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.