Matches in SemOpenAlex for { <https://semopenalex.org/work/W4291124803> ?p ?o ?g. }
- W4291124803 endingPage "304" @default.
- W4291124803 startingPage "302" @default.
- W4291124803 abstract "Extract Given real‐valued random variables X and Y whose arguments are conditions (‘events’) in a suitable probability space, their correlation coefficient ρ[X,Y] is defined as Cov[X,Y]/(σ[X]σ[Y]); their covariance Cov[X,Y] is in turn defined as E[XY]–E[X]E[Y], where E[X] is the expectation of X; the standard deviation σ[X] is defined as √ E[(X–E[X])2] (e.g. Parzen 1960: 362). Covariance is not itself an adequate measure of correlation; for example, any random variable is perfectly correlated with itself, but Cov[X,X] = σ[X]2, which varies. One must calibrate Cov[X,Y] by dividing by σ[X]σ[Y]. All these notions can be relativized to a set of background conditions by conditionalizing the underlying probabilities on those conditions. We must now define correlation coefficients for the conditions on which the probabilities are defined. Denote the probability of a condition C as P[C]. The indicator random variable X(C) is 1 if C obtains and 0 otherwise; thus..." @default.
- W4291124803 created "2022-08-13" @default.
- W4291124803 date "2002-10-10" @default.
- W4291124803 modified "2023-09-26" @default.
- W4291124803 title "Correlation Coefficients" @default.
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