Talk:Central moment

Moment around the origin is never defined. —Preceding unsigned comment added by 136.142.141.195 (talk • contribs)

Relation to moments about the origin


\mu_n = \sum_{j=0}^n {n \choose j} (-1) ^{n-j} \mu'_j \mu^{n-j}, $$ Enter n = 2

\mu_2 = \sum_{j=0}^2 {2 \choose j} (-1) ^{2-j} \mu'_j \mu^{2-j}, $$ Expand
 * $$\mu_2 = \mu'_0 \mu^{2} - 2 \mu'_1 \mu + \mu'_2$$

How is this equal to:
 * $$\mu_2 = \mu'_2 - \mu^2$$

Also:
 * $$\mu$$≠$$ \mu_0$$

From the definition we have
 * $$\mu_0 = \mu'_0$$ —Preceding unsigned comment added by 85.144.94.32 (talk) 09:50, 30 November 2009 (UTC)

Translation of the first central moment
I removed this property that is not true: « For n>1, the nth central moment is translation-invariant, i.e. for any random variable X and any constant c, we have:$$\mu_n(X+c)=\mu_n(X).\,$$ »

See for example, the property under Moment_(mathematics).

— Preceding unsigned comment added by Scharleb (talk • contribs) 13:16, 7 January 2024 (UTC)