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Algorithm 2.1 analysis approximation beta Box-Muller Brownian motion casino central limit theorem Chapter coin toss control variate converge covariance function cycle decimal expansion defined denote density function difference equation differential equations digits discussion distribution function error estimate event experiment Feller Figure finite fortune function F(x gambler gambler's ruin gambling gamma Gaussian time series Halton hit or miss inventory Knuth large numbers law of large length Lindgren linear congruential linear equation Markov chain Marsaglia Mathematical matrix middle-square MONTE CARLO INTEGRATION Monte Carlo method multivariate normal normal variate observations obtained path play points Poisson polynomial probabilistic probability density probability theory Program random numbers random sequence random walk random-number RANF reader sample mean Section sequence of random simulation solution St(A standard deviation standard normal variable stochastic processes Table techniques tion uniform variable uniformly distributed variable with parameter variate Monte Carlo Yakowitz