Regular Conditional Probability: Continuous Probability Distribution, Probability Measure, Random Variable - Couverture souple

 
9786131246296: Regular Conditional Probability: Continuous Probability Distribution, Probability Measure, Random Variable

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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. 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 [0,1], 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.

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