Paul was on the Rice faculty from 1947 until 1998, first as an instructor and, after receiving his PhD, as an assistant, then an associate, and since 1959, as a full professor.
In between, Paul earned a Bachelor of Divinity from the Perkins School of Theology at SMU in 1943. Pfeiffer, Professor Emeritus of Computational and Applied Mathematics, received his BS and MS in Electrical Engineering at Rice in 19, respectively, and his Ph.D. This material is not only important for computational purposes, but is also useful in displaying some of the structure of the relationships among events.
Since machine methods require precise formulation of problems in appropriate mathematical form, it is necessary to provide some supplementary analytical material, principally the so-called minterm analysis. In a few cases, alternate implementations are available in the Statistics Toolbox, but are implemented here directly from the basic MATLAB program, so that students need only that program (and the symbolic mathematics toolbox, if they desire its aid in evaluating integrals). Most of the programs developed here were written in earlier versions of MATLAB, but have been revised slightly to make them quite compatible with MATLAB 7. This should make the work useful as a stand-alone exposition as well as a supplement to any of several current textbooks. In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user defined MATLAB procedures and functions (which we refer to as m-programs, or simply programs) to solve many important problems in basic probability. And the symbolic toolbox, implementing MAPLE, may be used to evaluate integrals, if desired. Appendix B provides a convenient compendium of mathematical facts used frequently in this work.
#Matlab symbolic toolbox torrent how to
The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation. A few standard series and integrals are used, and double integrals are evaluated as iterated integrals. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. This is a "first course" in the sense that it presumes no previous course in probability.