(統計)抽樣分配

設 $X_1,X_2,\cdots,X_n$ $\stackrel{ iid}{\sim} N(\mu,\sigma^2)$，則$\overline{X}\ \sim N(\mu,\frac{\sigma^2}{n})$


$\mu$已知，$\cfrac{nS^2}{\sigma^2}\ \sim \chi^2(n)$，

$\mu$未知，用$\overline{X}$取代，$\cfrac{(n-1)S^2}{\sigma^2}\ \sim \chi^2(n-1)$

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設$X_1,X_2,\cdots,X_n$ $\stackrel{ iid}{\sim} N(\mu_1,\sigma_1^2)$

    $Y_1,Y_2,\cdots,Y_n$ $\stackrel{ iid}{\sim} N(\mu_2,\sigma_2^2)$

$\implies $ $\overline{X}- \overline{Y}\ \stackrel{ iid}{\sim}N(\mu_1-\mu_2,\frac{\sigma_1^2}{n}+\frac{\sigma_2^2}{n})$