Reposition the word only

[BigNerd]

I think in the following sentence the word 'only' occurs at the wrong position which changes the meaning of the statement inadvertently:

"Note that the new mean only depends on the conditioned variable, while the covariance matrix is independent from this variable. "

My impression is it should rather be as follows (placing the word 'only' before the words 'the new mean' rather than behind them):
"Note that only the new mean depends on the conditioned variable, while the covariance matrix is independent from this variable. "