subtraction of normal distributed stochastic variables
if we have set of stochastic variables representing the random time it takes to do something: X,Y,Z,W and C where C is the sum of X Y Z W, thus the time it takes to do these things in sequence. If:
makes C adding these together right, mean plus mean and std dev + std dev?
C: N(30+30+20+40,5+3+2+7)=N(120,17) is this correct?
subtraction is analogically, assuming we want to subtract W from C, naming it S we get:
is this also correct?
if yes, please link to a reliable source, i have googled but not found the proof other than the proof for addition.
would these operations also work for lognormally distributions?
edit: it seems like, in the case when the variables are independent, that the std deviation is ADDED also when subtracting. but i dont think these variables are independent. if they are not independent. is adding and subtraction of means same as before? here is adding std dev when they are dependent but it only explains the addition not subtraction
to simplify my question. will variation(std dev) be reduced to any extend if subtracting a dependent random variable from a sum of random dependent variables?