Distribution of Particles and Process Uncertainty

After obtaining the state probabilities and setting the distributional assumptions, it is interesting to simulate the probabilistic behavior of the system, i.e., evaluate Pr [Nj (t) = n], n = 0,. ..,oo and j = 1,2. For a given n, Pr [Nj (t) = n] is the joint probability of the n + 1 possible mutually exclusive events that i particles originated in compartment 1 AND n — i particles originated in compartment 2 are present in compartment j at t with i = 0. n. 

These profiles were normalized with respect to the initial condition in each compartment. The wider confidence intervals correspond to the initial conditions no, and the narrower confidence intervals to 10rro. Even without measurement error, fluctuations in the predicted amounts expressing the process uncertainty were observed the lower the number of molecules initially present in the compartments, the higher the observed fluctuations. 

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