Distribution of the product of $n$ i.i.d log-normal random variables

Asked May 20 '19 at 15:40

Active May 20 '19 at 15:54

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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 $$Y=X_1\times\cdots\times X_n$$

asked May 20 '19 at 15:40

s0ulr3aper07

1

You should be able to prove yourself that it is lognormal – kjetil b halvorsen May 20 '19 at 15:48
If not, just [search our site](https://stats.stackexchange.com/search?q=lognormal+product) for answers. – whuber May 20 '19 at 15:53
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? – s0ulr3aper07 May 20 '19 at 16:45

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