example 11.18 Three standard discrete distributions
open in the book ·
parts/02-mathematical-methods/09-probability-statistics.tex:503
· p. 376
- example -- no derivation owed by its kind
Rests on
-
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
definition 7.45
Series
¶
- depends_on definition 7.2 Absolute value ¶
- depends_on definition 7.4 Convergence ¶
-
depends_on
definition 11.3
Discrete random variable
¶
- depends_on definition 11.1 Discrete probability space ¶
-
depends_on
definition 7.45
Series
¶
-
depends_on
proposition 11.2
Elementary rules
¶
- depends_on definition 11.1 Discrete probability space ¶ ↺
- proves proof ch:09-probability-statistics@proof-1 ¶
- proves proof ch:09-probability-statistics@proof-2 ¶
-
depends_on
definition 11.4
Expectation
¶
-
depends_on
proposition 11.5
Transfer, linearity, monotonicity
¶
-
depends_on
proposition 11.12
Bilinearity
¶
-
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 proposition 11.5 Transfer, linearity, monotonicity ¶ ↺
- proves proof ch:09-probability-statistics@proof-5 ¶
-
depends_on
definition 11.11
Covariance and correlation
¶
-
depends_on
proposition 11.14
Independence implies zero covariance; the converse
fails
¶
-
depends_on
definition 11.13
Independence
¶
- depends_on definition 11.3 Discrete random variable ¶ ↺
- depends_on proposition 11.12 Bilinearity ¶ ↺
- proves proof ch:09-probability-statistics@proof-6 ¶
-
depends_on
definition 11.13
Independence
¶
Supports
- depends_on example 11.19 A counting 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 |
→ | Moments, variance, standard deviation | declared | parts/02-mathematical-methods/09-probability-statistics.tex:523 |
depends_on |
→ | Bilinearity | declared | parts/02-mathematical-methods/09-probability-statistics.tex:523 |
depends_on |
→ | Independence implies zero covariance; the converse fails | declared | parts/02-mathematical-methods/09-probability-statistics.tex:523 |
depends_on |
← | A counting measurement | declared | parts/02-mathematical-methods/09-probability-statistics.tex:552 |