Let $X_1,\ldots,X_n$ be independent log-normal random variables such that $$log(X_i)\sim N(\mu,\sigma^2)\ \ \forall i=1,\ldots,n$$

Then what can be said about the distribution of the random variable $Y$?

Where $Y$ is defined as $$Y=X_1\times\cdots\times X_n$$

  • 1
    $\begingroup$ You should be able to prove yourself that it is lognormal $\endgroup$ Commented May 20, 2019 at 15:48
  • $\begingroup$ If not, just search our site for answers. $\endgroup$
    – whuber
    Commented May 20, 2019 at 15:53
  • $\begingroup$ I already have an answer. As per my calculations, $logY\sim N(n\mu,n\sigma^2)$. However, the book I am using says the mean is $\mu$ instead of $n\mu$. Which is correct? $\endgroup$ Commented May 20, 2019 at 16:45


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