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Regular conditional probability : ウィキペディア英語版
Regular conditional probability
Regular conditional probability is a concept that has developed to overcome certain difficulties in formally defining conditional probabilities for continuous probability distributions. It is defined as an alternative probability measure conditioned on a particular value of a random variable.
==Motivation==
Normally we define the conditional probability of an event ''A'' given an event ''B'' as:
:P(A|B)=\frac.
The difficulty with this arises when the event ''B'' is too small to have a non-zero probability. For example, suppose we have a random variable ''X'' with a uniform distribution on (), and ''B'' is the event that X=2/3. Clearly the probability of ''B'' in this case is P(B)=0, but nonetheless we would still like to assign meaning to a conditional probability such as P(A|X=2/3). To do so rigorously requires the definition of a regular conditional probability.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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