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)#Transformation_of_center.

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