Question

If y follows log normal distribution, then log y follows normal distribution

Answer 1

I've got this density function of a log-normal random variable.

fX(x;σ)=1xσ2π−−√e−ln(x)22σ2fX(x;σ)=1xσ2πe−ln⁡(x)22σ2

I'm trying to find the density function of Y=lnXY=ln⁡Xand show that YY is distributed N(0,σ2)N⁡(0,σ2).

I know the normal distribution is as follows:

fX(x;σ)=12πσ2−−−−√e−(x−μ)22σ2fX(x;σ)=12πσ2e−(x−μ)22σ2

But I'm not sure how to proceed from the first equation to the second