Dear Users,
For normally distributed random variables x and y's p.d.f.:
\frac{1} {\sqrt{2\pi \sigma_x^2}}\exp\left\{- \frac{(x - \mu_x)^2}{2 \sigma_x^2}\right\}
and
\frac{1} {\sqrt{2\pi \sigma_y^2}}\exp\left\{- \frac{(y - \mu_y)^2}{2 \sigma_y^2}\right\}
What will be the p.d.f. of...
Integration of following (limit -∞ to +∞):
1/√(2πσ^2) ∫ln(x) * exp{-(x-μ)^2 / (2σ^2)} dx
After one-step (integration by parts) it looks like the following:
lnx + ∫ σ/(√2π) * exp[{-(x-μ)^2 / (2σ^2)} / {x (x-μ)}] dx
After another-step (by parts), it looks like the following:
lnx + ∫ 1/(√2πσ^2)...