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Normal and exponentialnormal (?) distribution 
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#1
Mar2812, 12:30 AM

P: 2

Dear Users,
For normally distributed random variables x and y's p.d.f.: [tex] \frac{1} {\sqrt{2\pi \sigma_x^2}}\exp\left\{ \frac{(x  \mu_x)^2}{2 \sigma_x^2}\right\} [/tex] and [tex] \frac{1} {\sqrt{2\pi \sigma_y^2}}\exp\left\{ \frac{(y  \mu_y)^2}{2 \sigma_y^2}\right\} [/tex] What will be the p.d.f. of ln(x)  ln(y)? Is there any method to find it? I think the followings are the p.d.f.s of u=ln(x) and v=ln(y) given x and y are normally distributed: [tex] \frac{1} {\sqrt{2\pi \sigma_x^2}}\exp\left\{u  \frac{(e^u  \mu_x)^2}{2 \sigma_x^2}\right\} [/tex] and [tex] \frac{1} {\sqrt{2\pi \sigma_y^2}}\exp\left\{v  \frac{(e^v  \mu_y)^2}{2 \sigma_y^2}\right\} [/tex] I am trying to find the p.d.f. of ln(x)ln(y). Any suggestions? 


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