proportionally to the probabilities vs As we have explained in section

These two phrases are not directly comparable as they serve different purposes. 'Proportionally to the probabilities' is used to describe a relationship between two variables, while 'as we have explained in section' is used to refer back to a previous explanation. They are both correct in their respective contexts.

Last updated: March 17, 2024

proportionally to the probabilities

This phrase is correct and commonly used in English to describe a relationship between two variables.

This phrase is used to indicate that something is changing in relation to the probabilities of certain outcomes. It is often used in statistical or mathematical contexts.

Examples:

The investment should be distributed proportionally to the probabilities of success for each project.
The size of the circles on the graph is scaled proportionally to the probabilities they represent.

Show examples from the web [+]

... the population, the offspring are generated by a crossover, a mutation or a reproduction proportionally to the probabilities cxpb, mutpb and 1 - (cxpb + mutpb ).
... the population, the offspring are generated by a crossover, a mutation or a reproduction proportionally to the probabilities cxpb, mutpb and 1 - (cxpb + mutpb ).
[0, 1) is partitioned into regions with lengths proportionally to the probabilities of the symbols. Any interval (that in turn can be represented by a number) that lies ...
Randomly choose a type of the fragment to be inserted proportionally to the probabilities of various fragment types to occur, and set its parameters (number of ...

As we have explained in section

This phrase is correct and commonly used in English to refer back to a previous explanation or information provided in a specific section.

This phrase is used to remind the reader or listener that the information being discussed has already been covered in a specific section of a document or presentation.

Examples:

As we have explained in section 2.1, the results of the study show a clear correlation between the variables.
As we have explained in the introduction, the purpose of this research is to investigate the impact of climate change on biodiversity.

Show examples from the web [+]

He appreciated, as we have explained in Section 3.1, that God's promises to Abraham were revealing the plan about Jesus which God had known from the ...
As we have explained in Section 4.3, PSTL uses its own wrapper class as a reference. Fortunately, this is identified by the compiler and thus can be corrected by ...
Aug 27, 1999 ... As we have explained in Section 2, the nontrivial structure of the gauge bundle is realized by the Wilson line (3). However, for our purpose, it is ...
As we have explained in Section 3 in some cases it is also necessary to update sibling classes although the superclass of a class has not been refactored.

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proportionally to the probabilities vs As we have explained in section