Bernoulli, binomial concept
| Definition | A Bernoulli variable is one with probability p and zero otherwise, with mean p and variance p(1 minus p). A binomial variable counts the ones among n independent Bernoulli trials, with mean np. Primer S, equation S.6. Also Bernoulli, binomial. |
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| Example | Ten fair coin flips show exactly seven heads with probability 120 over 1024, about 0.117. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id bernoulli-binomial, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation S.6. |
| Assumptions and scope | none |
| Prior art | none recorded |
| Evidence | none |
| Reviewed | semantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation S.6.
\[\Pr[X=k]=\binom{n}{k}p^{k}(1-p)^{n-k},\qquad \binom{n}{k}=\frac{n!}{k!\,(n-k)!},\qquad \mathbb E[X]=np.\]
Conditions
none
Ledger
none
First stated
Primer S section S.3 of Data Mining as Observation, added in draft 0.3 (2026-09-09) for the ECE 514 readers whose first courses are far behind. The idea is standard and TSK Appendix C covers it at length.
Measurements
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Failures and corrections
none
Invariance envelope
none declared
Machine checked
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Used in
Data Mining as Observation primer S.
Related
Poisson distribution; expectation; Monte Carlo.
See also
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Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.