What is the logic of using random numbers in simulation problems? For different set of random numbers different answers are obtained. I am studying simulation in operations research. I know the nature of experiments are all random and so and so theories. But I couldn't identify exact use of Random numbers. Please help anyone.
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One good example is evaluating $\int_0^1 f(u) du$ by interpreting the integral as the expected value of $f(U)$, where $U$ is a random variable that is uniformly distributed on $(0,1)$. You can generate a sample $u_1, \ldots, u_N$ from the uniform distribution on $(0,1)$, then compute the mean of the numbers $f(u_i)$ to approximate $E(f(U))$. – littleO May 09 '19 at 04:56
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Thats ok. Here is an eg. related to my question: A car operator finds that during the past few months the cars use has varied considerably. For the past 200 days a frequency distribution table is given. Then asked to simulate the demand for a 10 week period using random numbers. – Sreelakshmi K R May 09 '19 at 06:12
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Simulation is an alternative when analytic methods are difficult or infeasible, or simply as a check on analytic results. It would be difficult to solve your example problem analytically, so simulation is a good choice in this case. – awkward May 09 '19 at 17:20