proposition 11.17 Sampling identities
open in the book ·
parts/02-mathematical-methods/09-probability-statistics.tex:456
· p. 376
Rests on
-
depends_on
definition 11.16
Sample mean, variance and correlation
¶
-
depends_on
definition 11.11
Covariance and correlation
¶
-
depends_on
definition 11.6
Moments, variance, standard deviation
¶
-
depends_on
proposition 11.5
Transfer, linearity, monotonicity
¶
- depends_on definition 11.4 Expectation ¶
- depends_on proposition 11.2 Elementary rules ¶
- proves proof ch:09-probability-statistics@proof-2 ¶
-
depends_on
proposition 11.5
Transfer, linearity, monotonicity
¶
- depends_on proposition 11.5 Transfer, linearity, monotonicity ¶ ↺
-
depends_on
definition 11.6
Moments, variance, standard deviation
¶
-
depends_on
definition 11.13
Independence
¶
-
depends_on
definition 11.3
Discrete random variable
¶
- depends_on definition 11.1 Discrete probability space ¶
-
depends_on
definition 11.3
Discrete random variable
¶
- depends_on definition 11.6 Moments, variance, standard deviation ¶ ↺
-
depends_on
definition 11.11
Covariance and correlation
¶
-
depends_on
proposition 11.12
Bilinearity
¶
- depends_on definition 11.11 Covariance and correlation ¶ ↺
- depends_on proposition 11.5 Transfer, linearity, monotonicity ¶ ↺
- proves proof ch:09-probability-statistics@proof-5 ¶
-
depends_on
proposition 11.14
Independence implies zero covariance; the converse
fails
¶
- depends_on definition 11.13 Independence ¶ ↺
- depends_on proposition 11.12 Bilinearity ¶ ↺
- proves proof ch:09-probability-statistics@proof-6 ¶
- proves proof ch:09-probability-statistics@proof-8 ¶
Supports
- depends_on example 11.19 A counting measurement ¶
- depends_on example 11.31 A length measurement ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Sample mean, variance and correlation | declared | parts/02-mathematical-methods/09-probability-statistics.tex:466 |
depends_on |
→ | Bilinearity | declared | parts/02-mathematical-methods/09-probability-statistics.tex:466 |
depends_on |
→ | Independence implies zero covariance; the converse fails | declared | parts/02-mathematical-methods/09-probability-statistics.tex:466 |
depends_on |
← | A counting measurement | declared | parts/02-mathematical-methods/09-probability-statistics.tex:552 |
depends_on |
← | A length measurement | declared | parts/02-mathematical-methods/09-probability-statistics.tex:818 |
proves |
← | ch:09-probability-statistics@proof-8 | declared | parts/02-mathematical-methods/09-probability-statistics.tex:470 |