This is the first half of a text for a two semester course in mathematical statistics at the senior/graduate level for those who need a strong background in statistics as an essential tool in their career. To study this text, the reader needs a thorough familiarity with calculus including such things as Jacobians and series but somewhat less intense familiarity with matrices including quadratic forms and eigenvalues. For convenience, these lecture notes were divided into two parts: Volume I, Probability for Statistics, for the first semester, and Volume II, Statistical Inference, for the second. We suggest that the following distinguish this text from other introductions to mathematical statistics. 1. The most obvious thing is the layout. We have designed each lesson for the (U.S.) 50 minute class; those who study independently probably need the traditional three hours for each lesson. Since we have more than (the U.S. again) 90 lessons, some choices have to be made. In the table of contents, we have used a * to designate those lessons which are "interesting but not essential" (INE) and may be omitted from a general course; some exercises and proofs in other lessons are also "INE". We have made lessons of some material which other writers might stuff into appendices. Incorporating this freedom of choice has led to some redundancy, mostly in definitions, which may be beneficial.
The growth of neurochemistry, molecular biology, and biochemical genetics has led to a burgeoning of new information relevant to the pathogenesis of brain dysfunction. This explosion of exciting new information is crying out for collation and meaningful synthesis. In its totality, it defies systematic summa tion, and, of course, no one author can cope. Thus invitations for contributions were given to various experts in areas which are under active investigation, of current neurological interest, and pregnant. Although this project is relatively comprehensive, by dint of size, other topics might have been included; the selection was solely my responsibility. I believe systematic summation a virtual impossibility-indeed, hardly worth the effort. The attempt to assemble all of the sections involved in a large treatise with multiple authors inevitably results in untoward delays due to the difference in the rate at which various authors work. Therefore, the following strategy has been adopted: multiple small volumes and a relatively flexible format, with publication in order of receipt and as soon as enough chapters are assembled to make publication practical and economical. In this way, the time lag between the ideas and their emergence in print is the shortest.
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