Suppose that x has the lognormal distribution with parameters μ and σ2. find the distribution of 1/x.

Step-by-step 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

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step-by-step explanation: