Talk:Gauss's inequality

The article says this:
 * Let X be a unimodal random variable with mode m, and let $$\tau^2$$ be the expected value of $$(X-\tau)^2$$, which can also be expressed as $$(\mu - m)^2 + \sigma^2 $$, where $$\mu$$ and $$\sigma$$ are the mean and standard deviation of X.
 * Let X be a unimodal random variable with mode m, and let $$\tau^2$$ be the expected value of $$(X-\tau)^2$$, which can also be expressed as $$(\mu - m)^2 + \sigma^2 $$, where $$\mu$$ and $$\sigma$$ are the mean and standard deviation of X.

Several aspects of this make no sense.

It says "where $$\mu$$ and $$\sigma$$ are the mean and standard deviation of X, but it doesn't say what m is, and m is not referred to in any other place in the article that would even tacitly say what it is.

It says "let $$\tau^2$$ be the expected value of $$(X-\tau)^2$$". Notice how the Greek letter &tau; appears here twice. If you say "let &tau;2 be..." then whatever follows that should not depend on &tau; unless the statement somehow serves to define &tau; implicitly rather than explicitly.

It says "which can also be expressed as $$(\mu - m)^2 + \sigma^2 $$". Really. OK, look:

\begin{align} E((X-\tau)^2) & = E(((X-\mu)+(\mu-\tau))^2) \\ & = E((X-\mu)^2 + (X-\mu)(\mu-\tau) + (\mu - \tau)^2) \\ & = \sigma^2 + 0 + (\mu-\tau)^2. \end{align} $$

Could it be that what was meant was "let &tau;2 be the expected value of (X &minus; m)2? Michael Hardy (talk) 03:37, 14 May 2009 (UTC)


 * OK, I've concluded that that must be it. Michael Hardy (talk) 03:48, 14 May 2009 (UTC)
 * Yes you're right, that's what I meant to write. Apologies for not proofreading the article properly myself and thanks for spotting and correcting that. Qwfp (talk) 08:45, 14 May 2009 (UTC)

The article's punchline refers to Pr(|X|>k). Should it refer to Pr(|X-m|>k) ? Duoduoduo (talk) 14:53, 18 September 2009 (UTC)


 * I've changed it. The article in The American Statistician that was linked to assumes the mode is zero.  One may suspect that the person who wrote this followed that but neglected to state that assumption. Michael Hardy (talk) 15:12, 18 September 2009 (UTC)