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Second normal form (2NF), in database normalization, is a normal form. A relation is in the second normal form if it fulfills the following two requirements: A relation is in the second normal form if it fulfills the following two requirements:
This rule allows one to express a joint probability in terms of only conditional probabilities. [4] The rule is notably used in the context of discrete stochastic processes and in applications, e.g. the study of Bayesian networks, which describe a probability distribution in terms of conditional probabilities.
Codd introduced the concept of normalization and what is now known as the first normal form (1NF) in 1970. [4] Codd went on to define the second normal form (2NF) and third normal form (3NF) in 1971, [5] and Codd and Raymond F. Boyce defined the Boyce–Codd normal form (BCNF) in 1974. [6]
First normal form (1NF) is a property of a relation in a relational database. A relation is in first normal form if and only if no attribute domain has relations as elements. [ 1 ] Or more informally, that no table column can have tables as values.
Even if you provide a mathematical definition of 1NF, being in 1NF will be independent from being in 2NF. The quote from the article is wrong if 1NF is included. 2NF and higher are defined mathematically, and these definitions are such that for each i > j > 1, every database in iNF is also in jNF. Hence, for all NFs above 1, the quote is correct.
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Notice however that this rule may not be true if the involved differential entropies do not exist or are infinite. Joint differential entropy is also used in the definition of the mutual information between continuous random variables:
The relationship between this example and the chain rule is as follows. Let z , y and x be the (variable) positions of the car, the bicycle, and the walking man, respectively. The rate of change of relative positions of the car and the bicycle is d z d y = 2. {\textstyle {\frac {dz}{dy}}=2.}