## A Course in Computational Probability and StatisticsThis book arose out of a number of different contexts, and numerous persons have contributed to its conception and development. It had its origin in a project initiated jointly with the IBM Cambridge Scien tific Center, particularly with Dr. Rhett Tsao, then of that Center. We are grateful to Mr. Norman Rasmussen, Manager of the IBM Scientific Center Complex, for his initial support. The work is being carried on at Brown University with generous support from the Office of Computing Activities of the National Science Foundation (grants GJ-174 and GJ-7l0); we are grateful to Dr. John Lehmann of this Office for his interest and encouragement. Professors Donald McClure and Richard Vitale of the Division of Applied Mathematics at Brown University contributed greatly to the project and taught courses in its spirit. We are indebted to them and to Dr. Tore Dalenius of the University of Stockholm for helpful criticisms of the manuscript. The final stimulus to the book's completion came from an invLtation to teach a course at the IBM European Systems Research Institute at Geneva. We are grateful to Dr. J.F. Blackburn, Director of the Institute, for his invitation, and to him and his wife Beverley for their hospitality. We are greatly indebted to Mrs. Katrina Avery for her splendid secretarial and editorial work on the manuscript. |

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A Course in Computational Probability and Statistics Walter Freiberger,Ulf Grenander Limited preview - 2012 |

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ADDITIONAL OBSERVATION POINTS algorithm analysis analytically APL program Appendix approximation Assignment assume behavior chapter coefficients computational congruence constant continued fractions convergence corresponding covariance matrix denote dependence DEVIATION OF ESTIMATE discrete discussed distribution function equation equidistribution ESTIMATE VECTOR Figure Fourier frequency function function F given independent integral iteration large numbers LATEST ESTIMATE OCCURRED law of large linear look Markov chain mathematical mean square error mean value function MEASURE OF DEVIATION method Monte Carlo experiment Monte Carlo method multiplicative congruence normal distribution NUMBER OF OBSERVATIONS OCCURRED AT INDEX parameter periodogram plot polynomial possible probabilistic probability distribution probability theory problem properties pseudo-random numbers quadratic quadrature random numbers random sequences result Riemann-Lebesgue lemma sample SET ADDITIONAL OBSERVATION simulation space spectral density statistical stochastic variables tion trigonometric trigonometric polynomial VALUE OF LATEST VALUES AND LATEST variance