[contravariant]

A dynamical system is typically 100% internal state. It's just

1. A state space X

2. An evolution map f: X -> X

3. A measure \mu on X, preserved by f (such that f_*\mu = \mu) and where \mu(X) = 1.

To represent a series of i.i.d. random variables you can typically just represent them as a sequence of values with a joint probability distribution as the invariant measure.

If you've got a space X of such sequence you can also add the current value to it to get IR x X, with a map f: (x,t) -> x * 1.5 if t[0] is heads & x * 0.6 otherwise. But you'll have to tell me it's invariant measure because I can't come up with one.