Before revision:   ]  We present a general solution for the steady-state statistics of the number of enzyme molecules in the on and off states, and for the flip time (persistence ) distributions for this model switch .
After revision:  ] We present a general solution for the steady-state statistics of the number of enzyme molecules in the on and off states, for the general case where the enzyme can mediate flipping in either direction. For this general case we also solve for the flip time distribution, making a connection to first passage and persistence problems in statistical physics .