Biological molecule is perturbed by the external environment at all time, such as thermal fluctuation and noise. If the molecule has multiple states, the proportion of these states is a probability distribution when the system reaches equilibrium. Here we discuss the variance of the probability distribution of the multi-state system under external noise, and if the biological molecule is just the receptor on the membrane, the variance is the measurement uncertainty of the receptor. We derive the measurement uncertainty of multi-state system, and compare with the uncertainty of the equivalent lower-state model we used to use. The environmental noises include white noise, colored noise with varied correlation functions, and deterministic perturbations.