root-mean-square
If are real numbers, we define theirroot-mean-square or quadratic mean as
The root-mean-square of a random variable X is defined as the squareroot of the expectation of :
If are random variables with standard deviations, then the standard deviation oftheir arithmetic mean
, , is theroot-mean-square of .
Title | root-mean-square |
Canonical name | Rootmeansquare |
Date of creation | 2013-03-22 13:10:24 |
Last modified on | 2013-03-22 13:10:24 |
Owner | pbruin (1001) |
Last modified by | pbruin (1001) |
Numerical id | 4 |
Author | pbruin (1001) |
Entry type | Definition |
Classification | msc 26-00 |
Classification | msc 26D15 |
Synonym | root mean square |
Synonym | rms |
Synonym | quadratic mean |
Related topic | ArithmeticMean |
Related topic | GeometricMean |
Related topic | HarmonicMean |
Related topic | PowerMean |
Related topic | WeightedPowerMean |
Related topic | ArithmeticGeometricMeansInequality |
Related topic | GeneralMeansInequality |
Related topic | ProofOfGeneralMeansInequality |