hello 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: X: N(30,5) Y: N(30,3) Z: N(20,2) W: N(40,7) 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 the same, assuming we want to subtract W from C, naming it S we get: S: N(120-40,17-7)=N(80,10) 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. i dont understand this, take this example you have a washing machine and a drying machine, the time they take for doing a batch can be represented by a stochastic variable that are normally distributed and independent of each other. time it takes to wash your clothes Normaldist 45min std dev 5min time it takes to dry the clothes Normaldist 50min std dev 10min time it takes to wash and dry the clothes N(45+50,5+10) then if we want to subtract the time it takes to dry the clothes again we get N(45+50-50,5+10+5)= N(45,20) this does not make sense, why would it suddenly be more variation when washing the clothes? we use the same washing machine as before. The thing here is that washing and drying are separate processes in a sequence and they are not mixed together.