statistical mechanics - Physical intuition for independence of components of velocity in derivation of Maxwell–Boltzmann distribution

Maxwell derived the shape of the probability distribution of velocity of gas particles by starting with just two assumptions.

These are:

1. 
   

   The probability distribution is rotation invariant.

   
   


2. 
   

   The components (of velocity of a gas particle) in the direction of the coordinate axes are statistically independent.

   
   

And the rest is lovely deduction, but I found that as a layman I don't have any physical intuition as to why the second assumption is plausible. Is there an intuitive explanation behind the second assumption? If not, is there a way to derive the second assumption from a set of more plausible-looking assumptions?