Help with functions of random variables


New Member
The problem is basically from quantum mechanics, so apologies if the terminology is not correct.
So I have a random variable y with std and mean, SDy and Uy.
The random variable y is basically the number of particles in a volume with dimensions L*W*H.
Now SDy was generated using a 3 integrations over the three dimensions:
SDy = dl.dw.dh
which it will generate a formula in terms of L, W, and H.
So far L, W and H are considered constants.
If I want to look at population of volumes (this time) with different L, W, or H, the question would be how SDy can be calculated then? how the new assumption would impact SDy, given that L, W, and H are also represented by mean and stds.
thank you very much