A statistical model for the bifurcation of the radial electric field Er is developed in view of describing L–H transitions of tokamak plasmas. Noise in micro-fluctuations is shown to lead to random changes of Er, if a deterministic approach allows for more than one solution. The probability density function for and the ensemble average of Er are obtained. The L-to-H and the H-to-L transition probabilities are calculated, and the effective phase limit is derived. Due to the suppression of turbulence by shear in Er, the limit deviates from Maxwell's rule. The ensemble average of heat flux as well as that of Er do not show a hysteresis in contrast to the deterministic model. Experimental condition for observing the hysteresis is also addressed.