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For two probability measures, or two random variables, I wonder how their Signal-to-noise ratio distance is defined? I encounter this concept in Wikipedia.

For a probability measure on $\mathbb{R}$, its signal-to-noise ratio is defined as the ratio between its expectation and its deviation. But how is the distance defined in terms of the ratio?

Thanks and regards!

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    Yes, its undefined in that case but usually one would say that it is infinity. There is only signal but no noise, hence, its ratio is biggest possible, i.e. infinity.2012-04-24

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