Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

First of all, am I correct in assuming that given a normally distributed random variable A, and an independent log-normally distributed random variable B, the random variable A·B is normally distributed?

Assuming I am correct in that, I guess the resultant distribution has $\mu=\mu_a \mu_b$... what would the variance be? It doesn't quite seem like it should be $\sigma=\sigma_a \sigma_b$.

And if I'm incorrect in that, is there some other normal-esque distribution I can scale a normal RV by to keep the result normal?

share|cite|improve this question
Answer to first question: No. Hint on second question: $A$ and $B$ are independent and for any random variable $X$ with finite second moment, $\mathbb{V}\mathrm{ar}(X) = \mathbb{E} X^2 - (\mathbb{E} X)^2$. Pseudo-answer to third question: Well, if you're scaling random variable has a variance of zero, then the resulting product is still normally distributed. (But, this last comment is admittedly a little tongue-in-cheek.) Additional comment: Using the notation $A$ and $B$ for random variables is sufficiently nonstandard that it may confuse the casual reader. – cardinal May 10 '11 at 23:15

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.