Re: [問題] 積分..
※ 引述《dadayaki (DADA)》之銘言：
: f(y)=(1/c)e^(-y^2/2) y>=0
: =(1/C)e^(y^2/2) y<0
: (1)F(y)
: (2)P(y>0.5|y>0)
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this is a normal kernel
\int_{-\infty}^y \frac{1}{C}\exp\{-\frac{t^2}{2}\}dt
= \frac{1}{C}\frac{sqrt{2\pi}}{2\pi}\exp\{-\frac{t^2}{2}\}dt
= \frac{\sqrt{2\pi}}{C}\Phi(y) for (y < 0)
Similarly,
\int_{\-infty}^y = \frac{\sqrt{2\pi}}{2C} +
\int_0^y \frac{1}{c}\exp\{-\frac{t^2}{2}\}dt
= \frac{\sqrt{2\pi}}{2C} + \frac{\sqrt{2\pi}}{c}(Phi(y) - \frac{1}{2})
= \frac{\sqrt{2\pi}}{2}(\frac{1}{C}-\frac{1}{c}) +\frac{\sqrt{2\pi}}{c}\Phi(y)
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