# Help on understanding sum of independent variables(new to statistics)

#### KelvinG

##### New Member
Hello everybody. Im new to stat. Lets say i have an independent random variable X and Im having difficulties on wrapping around the idea on the difference between say 5X in comparison to (x1+x2+x3+x4+x5) on their difference.

Like for the derivation of the standard error although i understand in when i look at it but in my mind theres this other scenario playing like why cant it be like var((x1+x2+x3+x4+x5)/5)=var(5x/5) though it doesnt make sense since on the first one youll get the SE= (sigma)/sqrt(5) on the other hand what will be left on var(5x/5)= just var(x) which will be just SE = sigma. I know its wrong but i feel im having difficulty finding the second one as not true because i might be missing or have not learned a fundamental principle.

#### rogojel

##### TS Contributor
hi,
if I understand your question correctly the answer is that the equation x1+x2+x3+x4+x5 = 5*x is not valid. the x1 , x2 etc are the same random variable in the sense that they have the same distribution, but the actual values will be different - as in running the same random number generator 5 times. Obviously you will get 5 different values. 5*x would mean that you generate a single random value and add that one value 5 times - something completely different.

regards