統計

\(\displaystyle \frac{\bar{y}-\mu_B}{s_y/\sqrt{15}}\sim t(14)\)より、上限下限は、 \(\displaystyle \bar{y} \pm t_{0.025}\frac{s_y}...

\(M_X(t)\) \(M_X(t)\)\(=E\) \(=\displaystyle \sum^\infty_{x=0} e^{tx}\frac{\lambda^x}{x!}e^{-\lambda}\) \(=\displaystyle...

\(X \sim N(\mu,\sigma^2)\)の製品を1つ検査した時に良品である確率は、 \(P(S_L \leq X \leq S_U)\)\(\displaystyle = \int ^{\frac{S_U-\mu}{\sigma...

\(\displaystyle E=E\left\) \(\displaystyle =\sum_{j=0}^\infty g_j E\left\)\(=0\) \(Cov\)\(=E-EE\) \(=E\) \(\displaystyle...

\(E=E\)(ただし、\((i,j)=(1,1)\)\(,(2,2)\)\(,(3,5)\)) \(=E-E\) \(=E\)\(-E\) \(=\tau_1-\tau_2\) また、 \(V=V\) \(=V\) \(=V+V\)\(=...

\(\displaystyle \bar{X}=\frac{m\bar{X}_{(0)}+(n-m)\bar{X}_{(1)}}{n}\)を\((2)\)式に代入して示される。 \(\displaystyle d^2=\frac{SS_B}...

\(X \sim B(n,\theta)\)で、 \(V=n\theta(1-\theta)\)より、 \(\displaystyle V=V\left\) \(\displaystyle =\frac{\theta(1-\theta)}{...

\(b_0\) \(\displaystyle E=E\left\) \(\displaystyle =E\left\) \(\displaystyle = \beta+\frac{1}{n}\sum_{i=1}^n E\left\) \(...

\(\displaystyle E=\int^\infty_0 xf(x)dx\) \(\displaystyle =\int^\infty_0 x\lambda e^{-\lambda x}dx\)\(\displaystyle = \f...

\(\mu=\ln \theta\)なので、\(X \sim N(\ln \theta, 1)\)で、 \(L(\theta)=\displaystyle \prod_{i=1}^n f(x_i)\) \(\displaystyle = \...