6.6: Sura Vitu muhimu
- Page ID
- 179216
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- Usambazaji wa kawaida
- kuendelea random variable\((RV)\) na pdf\(f(x) =\)
\[\frac{1}{\sigma \sqrt{2 \pi}} \mathrm{e}^{\frac{-(x-\mu)^{2}}{2 \sigma^{2}}}\nonumber\]
, wapi\(\mu\) maana ya usambazaji na\(\sigma\) ni kupotoka kwa kawaida; notation:\(X \sim N(\mu, \sigma)\). Kama\(\mu = 0\) na\(\sigma = 1\), the\(RV\)\(Z\), inaitwa kiwango usambazaji wa kawaida.
- Usambazaji wa kawaida wa kawaida
- kuendelea random variable\((RV) X \sim N(0, 1)\); wakati\(X\) ifuatavyo kiwango usambazaji wa kawaida, ni mara nyingi alibainisha kama\(Z \sim N(0, 1)\).
- z-alama
- mabadiliko ya mstari wa fomu\(z=\frac{x-\mu}{\sigma}\) au imeandikwa kama\(z=\frac{|x-\mu|}{\sigma}\); ikiwa mabadiliko haya yanatumika kwa usambazaji wowote\(X \sim N(\mu, \sigma)\) wa kawaida matokeo ni usambazaji wa kawaida wa kawaida\(Z \sim N(0,1)\). Kama mabadiliko haya ni kutumika kwa thamani yoyote maalum\(x\) ya\(RV\) na maana\(\mu\) na kiwango kupotoka\(\sigma\), matokeo inaitwa z-alama ya\(x\). Alama ya z-inatuwezesha kulinganisha data ambayo kwa kawaida husambazwa lakini imeongezwa tofauti. Alama ya z-ni idadi ya upungufu wa kawaida hasa\(x\) ni mbali na thamani yake ya maana.