Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

If $X_1,\ldots,X_n$ are dependent normal random variables, what would be the distribution of $X_1+\ldots+Xn$? Is it still normal?

share|improve this question

1 Answer 1

up vote 0 down vote accepted

It depends on how they are dependent.

The answer is yes if they are multivariate normal but not always in general.

share|improve this answer
    
@May: if they are independent (as in the first i of iid) then $\sum_i \sum_j X_i Y_j = \sum_i X_i \times \sum_j Y_j $. So if they are normally distributed then you have the product of two normal random variables, which is in general not normally distributed –  Henry Nov 16 '12 at 0:52

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.