Consider the second-order reaction shown in Eqn. (10.73). Since it is not possible to find the variance and average analytically, it is necessary to perform a stochastic simulation to estimate the size of the fluctuations in a micro-reactor. Using MATLAB, Mathematica, Basic, FORTRAN, or some other tool, write a short program to simulate the average of several realizations of the reaction. Assume that k1 = 4k2, and that the initial molecule numbers are ˜NA = ˜N◦ A, and ˜NB = 0. Compare your results for the average with those that arise in the thermodynamic limit (i.e. the usual dcA/dt ∼ −k1c2 A +· · · ). You should first write the code to repeat the example in Section 10.10. When you are able to reproduce the results there, it is a small change to simulate the second-order reaction.