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In the final project we are going to simulate the radioactive decay of these nuclei using sampling through random numbers. We assume that at t=0 we have NX(0) nuclei of the type X which can decay radioactively. At a given time t we are left with NX(t) nuclei. With a transition rate X, which is the probability that the system will make a transition to another state during a time step of one second, we get the following differential equation whose solution is dNX(t)=XNX(t)dt, NX(t)=NX(0)eXt, and where the mean lifetime of the nucleus X is =X1. If the nucleus X decays to Y, which can also decay, we get the following coupled equations: dNX(t)/dt=XNX(t),anddNY(t)/dt=YNY(t)+XNX(t). We assume that at t=0 we have NY(0)=0. In the beginning we will have an increase of NY nuclei, however, they will decay thereafter. In this project we let the nucleus 210Bi represent X. It decays through -decay to 210Po, which is the Y nucleus in our case. The latter decays through emission of an -particle to 206Pb, which is a stable nucleus. 210Bi has a mean lifetime of 7.2 days while 210 Po has a mean lifetime of 200 days. 2. Make a program which solves the above equations employing in-situ Monte Carlo simulations (we should compare the transition rates with random numbers). Compare the results from your program with the exact answer as function of NX(0)=1000. Make plots of your results