Chapter 6, Problem 111SE

a.

To determine

Show that the density function for Y is $f\left(y\right)=\left(\frac{1}{y\sigma \sqrt{2\pi }}\right)e^{\frac{-{\left(\ln y-\mu \right)}^2}{2{\sigma }^2}},y>0$.

b.

To determine

Show that $E\left(Y\right)=e^{\mu +\frac{{\sigma }^2}{2}}$.

Show that $V\left(Y\right)=e^{2\mu +{\sigma }^2}\left(e^{{\sigma }^2}-1\right)$.