Mathematics, such as probability theory, is to standardize x* and y*. But isn't standardization only available in normal distribution? Then what should I do?
This does not affect the problem. Generally called standardization, different places have different names. Also called zeroing whitening. You don't have to worry too much about it. You can do this operation without normal distribution!
After processing, the mean and variance can be calculated directly through the formula.
For example, E(x*)
=E[x-E(x)/√D(x)]
=[E(x)-E(E(x))/√D(x)]
=[E(x)-E(x)]/√D(x)
=0