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statistik:mittelpunkt [2012/05/26 18:59] – phreazer | statistik:mittelpunkt [2014/02/11 21:49] (current) – external edit 127.0.0.1 | ||
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===== Zentrales Moment ===== | ===== Zentrales Moment ===== | ||
- | $$ E((X-\bar{X})^k = 0 $$ | + | $$ E((X-\bar{X})^k) = 0 $$ |
+ | |||
+ | Für k = 2 => Varianz: | ||
+ | |||
+ | $$\sigma^2 = E((X-\mu)^2) $$ | ||
+ | |||
+ | als korrigierte Stichprobenvarianz $s^2$ mit n-1 Freiheitsgraden (df), falls $\mu$ unbekannt | ||
+ | |||
+ | $$s^2 = \frac{1}{n-1} \sum_{i=1}^n (X_i - \bar{X})^2$$ | ||
+ | |||
+ | sonst, falls $\mu$ bekannt | ||
+ | |||
+ | $$s^{*2} = \frac{1}{n} \sum_{i=1}^n (X_i - \mu)^2$$ | ||
====== Arithmetisches Mittel der Grundgesamtheit ====== | ====== Arithmetisches Mittel der Grundgesamtheit ====== | ||
- | $$ \mu = \frac{\sum_{n=1}^n X_i}{N} | + | $$ \mu = \frac{\sum_{n=1}^n X_i}{N} |
===== Zentrales Moment ===== | ===== Zentrales Moment ===== | ||
- | $$ E((X-\eta)^k) = 0 $$ | + | $$ E((X-\eta))^k = 0 $$ |