Initialization of object static members

Question

Static members confuse me sometimes. I understand how to initialize a simple built in type such as int with something along the lines of int myClass::statVar

Answer 1

If only myClass needs the RandomGenerator, then:

myClass::myClass()
{
    itsGenerator.Randomize();
}

Does it matter if you re-randomize your random generator for each object? I'm assuming no ;-)