I have the following question on an exercise sheet:
Let $x = 4y$. One student claims $\sigma_x = 4\sigma_y$. Another claims that since $ x = y + y + y + y$, then $\sigma_x = 2\sigma_y$. Who is correct and why is the other person wrong?
I'm think the first student is correct because just intuitively, if you multiply your data points by 4, then the spread becomes 4 times larger (I also did linear coding before and was told this).
However, I am not sure how the student even gets from $ x = y + y + y + y$ to $\sigma_x = 2\sigma_y$. Can anyone help me see what the mistake is or even how they have made this leap?
(also a proof of the first student's claim or a link to a proof would be appreciated!)