# A problem about normal distribution, independent random variables

Suppose $\alpha_1, ..., \alpha_n$ are independent identically distributed random variables, $a_1, ..., a_n,b_1,...,b_n$ are non-zero constants. Is it true that if $\sum_{i=1}^{n}a_i\alpha_i$ and $\sum_{i=1}^{n}b_i\alpha_i$ are independent, then $\alpha_1, ..., \alpha_n$ are normal variables?

• Can anyone explain me why was this question closed? Apr 23, 2017 at 15:48
• It wasn't even a question. Apr 23, 2017 at 19:33

This is called the Darmois-Skitovich theorem. Of course, one needs to add the condition that $a_jb_j\neq 0$.