Chapter 10

Inequalities and limit theorems

“What should I do if I can’t calculate a probability or expectation exactly?” Almost everyone who uses probability has to deal with this sometimes. Don’t panic. There are powerful strategies available: simulate it, bound it, or approximate it.

  • Simulations using Monte Carlo: We have already seen many examples of simulations in this book; the R sections give numerous examples where a few lines of code and a few seconds on a computer suffice to get good approximate answers. “Monte Carlo” just means that the simulations use random numbers (the term originated from the Monte Carlo Casino in Monaco).

    Monte Carlo simulation is an extremely powerful technique, and there are many problems where it is the only ...

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