Answer:

Explanation:
For this case we know that the distribution for the random variable is given by:

The density function for the log normal random variable is given by:

And we want to find the distribution for the random variable

In order to find this distribution we can use the cumulative distribution function like this:
Let
, if we solve for X from this transformation we got:

And then we have this:

And we can find the density function as the derivate of the distribution function like this:


But we see that we don't have an specified form for the distribution
If we assume that X follows a normal distribution
and we use the transformation
we see that X follows a log normal distribution. And we see that:

And if we find the distribution of
we got this:



And then we see that
