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\[\phi(-\frac{\ln(m)}{\sqrt{v}}+\frac{\sqrt{v}}{2})=\frac{1}{\sqrt{2\pi}}\exp(-\frac{1}{2}[-\frac{\ln(m)}{\sqrt{v}}+\frac{\sqrt{v}}{2}]^2)\]
\[=\frac{1}{\sqrt{2\pi}}\exp(-\frac{1}{2}[(\frac{\ln(m)}{\sqrt{v}}+\frac{\sqrt{v}}{2})-\frac{2\ln(m)}{\sqrt{v}}]^2)\]
\[=\frac{1}{\sqrt{2\pi}}\exp(-\frac{1}{2}[(\frac{\ln(m)}{\sqrt{v}}+\frac{\sqrt{v}}{2})^2-\frac{4\ln(m)}{\sqrt{v}}(\frac{\ln(m)}{\sqrt{v}}+\frac{\sqrt{v}}{2})+(\frac{2\ln(m)}{\sqrt{v}})^2])\]
\[=\frac{1}{\sqrt{2\pi}}\exp(-\frac{1}{2}[(\frac{\ln(m)}{\sqrt{v}}+\frac{\sqrt{v}}{2})^2-2\ln(m)])\] |
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发表于 2017-5-1 04:58
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