Monte Carlo simulation is also known as probability simulation. It is a method used to understand the effects of uncertainty and risk in project management, business finance, cost and many other models used in forecasting. Monte Carlo simulation is named after a city in Monaco. In this city the primary attractions are games of chance such as casinos. Gambling games such as roulette, slot machines and dice show random behavior and are therefore good applications of Monte Carlo simulation.[THESE ARE NOT Necessary ] Simulation of radioactive decay is a truly random process. In this problem, the probability of decay remains constant independent of the life of the nuclei. The probability that nuclei undergo radioactive decay in time change in t is p. The problem considers a system with N0 unstable nuclei in at the start. The question is involves showing how the parent nucleus (N) change with respect to time. [there N number of unstable nucleus, its not about only one nucleus ] Pseudo code refers to a method often used to describe an algorithm. Pseudo code looks like a computer program but it is normally not written using a specific language. It helps the programmer in representing the program clearly. It distracts the focus of the programmer from the syntax requirements of a certain programming language. The pseudo code for radioactive decay simulation is shown below. It can be used for computing iteratively the varying number of nuclides. [All of these are coping form the website and not needed] i) Input number of nuclides N0 at the start ii) Enter decay constant λ iii) Enter number of time steps M iv) Enter time step dt v) Loop: i from zero to M vi) Loop: j from zero to Ni vii) Generate random numbers represented by r viii) If r<λ∗dt then N_{i}=N_{i}-1 ix) Output i∗dt and Ni to a file x) N_{i+1}=N_{i} xi) Plot Ni vs. i∗dt for all i [not needed in this way.] The pseudo code shown above is intended which helps in indicating the structure of the algorithm. It can be made clearer by following the simplified version of the algorithm shown below. Loop from time t=0 to time t, that represents step change t Loop over the remaining parent nuclei Make a decision whether the nucleus decays: If the random change in time t is less than change in time t then, Reduce the number of parents by one End if the condition end loop over nuclei is reached Record or plot record N versus time T Otherwise, end loop over time The algorithm used for radioactive Monte Carlo simulation can be represented as shown below. If N is the number of radioactive nuclei available at time t, then the equation showing the rate of decay is represented as, 1 represents the decay constant and the solution to the differential equation shown above is given by, N (t) = N0 exp (-lt). N0 represents the number of radioactive nuclei available at time t=0. Radioactivity is random in nature which makes it possible to model decay using Monte Carlo simulation technique. At any period of time t, all available radioactive nuclei remaining from the sample possess an equal decay probability. This decay probability can be obtained by rearranging the above rate equation. The next thing to do is to generate N random numbers and compare them with l*dt. If the random numbers generated are less than l*dt, an assumption is made that decay has taken place. Therefore, it is possible to predict the number of radioactive nuclei which have undergone decay during the interval dt. This process is repeated to get the number of nuclei which would decay in the next interval. Monte Carlo simulation uses any many procedures in using random numbers. It can be used in simulating natural phenomena and simulation of apparatus in experiments using numerical analysis.[none sence] In this problem the exponential decay is derived which describes the average for a large number of nuclei, but it becomes very inaccurate as the number of nuclei gets small. Radioactive decay is ``spontaneous'', that is, it happens independent of external stimulation. As the probability of decay reduces in time t, the number of nuclei present also decreases. The actual decay process is random (the rate for each period fluctuates). A Geiger counter is very useful in radioactive decay. It counts the number of nuclei that decay during a given period of time.[I have no clue where he got this ] In some circumstances, a range of values can be estimated. For example, in a radioactive decay project, one might estimate the time it will take to complete a particular task; based on some known knowledge, one can also estimate the absolute maximum time it could take, in the worst possible circumstance, and the absolute minimum time, in the best possible circumstance. The same could be done for other Monte Carlo simulation experiments. For instance, in a financial market, one might know the distribution of possible values through the standard and mean values of returns. [I have no idea what witer is talking about] By using a range of possible values, instead of a single guess, one can create a more realistic picture of what might happen in the future. When a model is based on ranges of estimates, the output of the model will also be a range.[it doesn’t mean anything] This is quite different from a normal forecasting model, in which one starts with some fixed estimates – say the time t it will take to complete each of three parts of a project – and end up with another value N – the total time for the project. If the same model were based on ranges of estimates for each of the three parts of the project, the result would be a range of times it might take to complete the project. When each part has a maximum and minimum estimate, we can use those values to estimate the total maximum and minimum time for the project. When one has a range of values as a result, one begins to understand the risk and uncertainty in the model. The major feature of a Monte Carlo simulation is that it can advise a person on how to create the ranges of estimates. In radioactive Monte Carlo simulation, a spontaneous value is selected for each of the problems, based on the range of estimates. The model is computed based on this spontaneous value. The process is repeated and the result of the model is recorded. A typical Monte Carlo simulation calculates the model thousands or hundreds of times, each time using different spontaneously-chosen values. When the radioactive simulation is complete, we have a huge number of results from the model, each based on spontaneous input values. These results are used to describe the probability, or likelihood, of reaching various results from the radioactive decay simulation model.[I have no idea where he/she got this info] 1. M.P. Allen and D. J. Tildesley, Computer Simulation of Liquids, OUP, Oxford, 1987, pages 110-112. 2. D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, CUP, 2000, pages 1-4 and 48-53. 3. D. Frenkel and B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, Academic Press, San Diegio, 1996, pages 19-28. 4. R.J. Sadus, Molecular Simulation of Fluids: Theory, Algorithm and Object- Orientation, Elsevier, Amsterdam, 1999 5. W.H. Press, B.F. Flannery, S. A. Teukolsky and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, CUP, Cambridge, 1988, pages 204-213 -

Monte Carlo simulation is also known as probability simulation. It is a method used to understand the effects of uncertainty and risk in project management, business finance, cost and many other models used in forecasting. Monte Carlo simulation is named after a city in Monaco. In this city the primary attractions are games of chance such as casinos. Gambling games such as roulette, slot machines and dice show random behavior and are therefore good applications of Monte Carlo simulation.[THESE ARE NOT Necessary ]
Simulation of radioactive decay is a truly random process. In this problem, the probability of decay remains constant independent of the life of the nuclei. The probability that nuclei undergo radioactive decay in time change in t is p. The problem considers a system with N0 unstable nuclei in at the start. The question is involves showing how the parent nucleus (N) change with respect to time. [there N number of unstable nucleus, its not about only one nucleus ]
Pseudo code refers to a method often used to describe an algorithm. Pseudo code looks like a computer program but it is normally not written using a specific language. It helps the programmer in representing the program clearly. It distracts the focus of the programmer from the syntax requirements of a certain programming language. The pseudo code for radioactive decay simulation is shown below. It can be used for computing iteratively the varying number of nuclides. [All of these are coping form the website and not needed]

i) Input number of nuclides N0 at the start
ii) Enter decay constant λ
iii) Enter number of time steps M
iv) Enter time step dt
v) Loop: i from zero to M
vi) Loop: j from zero to Ni
vii) Generate random numbers represented by r
viii) If r<λ∗dt then N_{i}=N_{i}-1
ix) Output i∗dt and Ni to a file
x) N_{i+1}=N_{i}
xi) Plot Ni vs. i∗dt for all i
[not needed in this way.]
The pseudo code shown above is intended which helps in indicating the structure of the algorithm. It can be made clearer by following the simplified version of the algorithm shown below.
Loop from time t=0 to time t, that represents step change t
Loop over the remaining parent nuclei
Make a decision whether the nucleus decays:
If the random change in time t is less than change in time t then,
Reduce the number of parents by one
End if the condition end loop over nuclei is reached
Record or plot record N versus time T
Otherwise, end loop over time
The algorithm used for radioactive Monte Carlo simulation can be represented as shown below.
If N is the number of radioactive nuclei available at time t, then the equation showing the rate of decay is represented as,

1 represents the decay constant and the solution to the differential equation shown above is given by, N (t) = N0 exp (-lt). N0 represents the number of radioactive nuclei available at time t=0. Radioactivity is random in nature which makes it possible to model decay using Monte Carlo simulation technique. At any period of time t, all available radioactive nuclei remaining from the sample possess an equal decay probability. This decay probability can be obtained by rearranging the above rate equation.

The next thing to do is to generate N random numbers and compare them with l*dt. If the random numbers generated are less than l*dt, an assumption is made that decay has taken place. Therefore, it is possible to predict the number of radioactive nuclei which have undergone decay during the interval dt. This process is repeated to get the number of nuclei which would decay in the next interval.
Monte Carlo simulation uses any many procedures in using random numbers. It can be used in simulating natural phenomena and simulation of apparatus in experiments using numerical analysis.[none sence]
In this problem the exponential decay is derived which describes the average for a large number of nuclei, but it becomes very inaccurate as the number of nuclei gets small. Radioactive decay is “spontaneous”, that is, it happens independent of external stimulation. As the probability of decay reduces in time t, the number of nuclei present also decreases. The actual decay process is random (the rate for each period fluctuates). A Geiger counter is very useful in radioactive decay. It counts the number of nuclei that decay during a given period of time.[I have no clue where he got this ]
In some circumstances, a range of values can be estimated. For example, in a radioactive decay project, one might estimate the time it will take to complete a particular task; based on some known knowledge, one can also estimate the absolute maximum time it could take, in the worst possible circumstance, and the absolute minimum time, in the best possible circumstance. The same could be done for other Monte Carlo simulation experiments. For instance, in a financial market, one might know the distribution of possible values through the standard and mean values of returns. [I have no idea what witer is talking about]
By using a range of possible values, instead of a single guess, one can create a more realistic picture of what might happen in the future. When a model is based on ranges of estimates, the output of the model will also be a range.[it doesn’t mean anything]

This is quite different from a normal forecasting model, in which one starts with some fixed estimates – say the time t it will take to complete each of three parts of a project – and end up with another value N – the total time for the project. If the same model were based on ranges of estimates for each of the three parts of the project, the result would be a range of times it might take to complete the project. When each part has a maximum and minimum estimate, we can use those values to estimate the total maximum and minimum time for the project. When one has a range of values as a result, one begins to understand the risk and uncertainty in the model. The major feature of a Monte Carlo simulation is that it can advise a person on how to create the ranges of estimates.
In radioactive Monte Carlo simulation, a spontaneous value is selected for each of the problems, based on the range of estimates. The model is computed based on this spontaneous value. The process is repeated and the result of the model is recorded. A typical Monte Carlo simulation calculates the model thousands or hundreds of times, each time using different spontaneously-chosen values.
When the radioactive simulation is complete, we have a huge number of results from the model, each based on spontaneous input values. These results are used to describe the probability, or likelihood, of reaching various results from the radioactive decay simulation model.[I have no idea where he/she got this info]

1. M.P. Allen and D. J. Tildesley, Computer Simulation of Liquids, OUP, Oxford,
1987, pages 110-112.
2. D. P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical
Physics, CUP, 2000, pages 1-4 and 48-53.
3. D. Frenkel and B. Smit, Understanding Molecular Simulation: From
Algorithms to Applications, Academic Press, San Diegio, 1996, pages 19-28.
4. R.J. Sadus, Molecular Simulation of Fluids: Theory, Algorithm and Object-
Orientation, Elsevier, Amsterdam, 1999
5. W.H. Press, B.F. Flannery, S. A. Teukolsky and W. T. Vetterling, Numerical
Recipes in C: The Art of Scientific Computing, CUP, Cambridge, 1988, pages
204-213

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