Hi, I am curious as to the strategy for integrating the lognormal function to calculate the mean.(adsbygoogle = window.adsbygoogle || []).push({});

The integral to be solved is:

[tex]\frac{1}{S\sqrt{2\pi}}\int_{0}^{\infty} \frac{e^{(lnx-M)^{2}}}{2S^{2}} dx [/tex]

I was trying to do it by a substitution

[tex]y=lnx\;\rightarrow\;dy=\frac{1}{x}dx[/tex]

[tex]x=e^{y}\;\rightarrow\;dx=e^{y}dy[/tex]

to give

[tex]\frac{1}{S\sqrt{2\pi}}\int_{-\infty}^{\infty} \frac{e^{(y-M)^{2}}}{2S^{2}}e^{y} dy [/tex]

and then integration by parts, but I keep going round in circles with vdu and what not…

Can anyone enlighten me on the trick to this?

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# Derivation of Lognormal mean

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