1 introduction
exercises
2 elements of probability
2.1 sample space and events
2.2 axioms of probability
2.3 conditional probability and independence
2.4 random variables
2.5 expectation
2.6 variance
2.7 chebyshev's inequality and the laws of large numbers
2.8 some discrete random variables
2.9 continuous random variables
2.10 conditional expectation and conditional variance
3 random numbers
3.1 pseudorandom number generation
3.2 using random numbers to evaluate integrals
4 generating discrete random variables
4.1 the inverse transform method
4.2 generating a poisson random variables
4.3 generating binomial random variables
.4.4 the acceptance-rejection technique
4.5 the compositon approach
4.6 generating random vectors
5 generating continuous random variables
5.1 the inverse transform algorithm
5.2 the rejecton method
5.3 the polar method for generating normal random variables
5.4 generating a poissn process
5.5 generating a nonhomogeneous poisson process
6 the discrete event simulation approach
7 statistical analysis of simulated data
8 variance reduction techniques
9 statistical validation techniques
10 markov chain monte carlo methods
11 some additional topics
index
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