An Introduction to Probability Theory and its Applications, Volume I

Arthur Chickering is Distinguished Professor of Higher Education at Memphis State University. On leave from the Directorship of the Center for the Study of Higher Education at Memphis State, he is Visiting Professor at George Mason University. Zelda Gamson is a sociologist who holds appointments at the John W. McCormack Institute of Public Affairs at the University of Massachusetts-Boston and in the Center for the Study of Higher and Postsecondary Education at the University of Michigan.

Seven Principles for Good Practice in Undergraduate Education: Faculty Inventory. Institutional Inventory.

It represents a universally applicable attitude and skill set everyone, not just computer scientists, would be eager to learn and use.

/pdf/computational-thinking-ji-suan-lun-de-si-kao-3qvv34ha3s.pdf

Computational Thinking 計算論的思考

Statistical Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 124, 254, 297 History Corner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20, 179 Teacher’s Corner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26, 173, 263, 335 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40, 147, 211, 366 Statistical Computing and Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Statistical Computing and Software Reviews . . . . . . . . . . . . . . . . . . . . . . . . 75, 187 Reviews of Books and Teaching Materials . . . . . . . . . . . . . . . . . 92, 189, 281, 401 Brief Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100, 195, 292, 404 Letters to the Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102, 197, 294, 406 Special Section: Statistical Training and Curricular Revision . . . . . . . . . . . . . 105 Errata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 Special Section: Opportunities and Challenges for the Discipline . . . . . . . . . 201 Software Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

The American statistician

/pdf/aufgaben-und-lehrsatze-aus-der-analysis-mva9fm8nx4.pdf

Aufgaben und Lehrsätze aus der Analysis

We study the joint distribution of the number of occurrences of members of a collection of nonoverlapping motifs in digital data. We deal with finite and countably infinite collections. For infinite collections, the setting requires that we be very explicit about the specification of the underlying measure-theoretic formulation. We show that (under appropriate normalization) for such a collection, any linear combination of the number of occurrences of each of the motifs in the data has a limiting normal distribution. In many instances, this can be interpreted in terms of the number of occurrences of individual motifs: They have a multivariate normal distribution. The methods of proof include combinatorics on words, integral transforms, and poissonization.

On the Variety of Shapes in Digital Trees

A sequence of geometric random variables of length $n$ is a sequence of $n$ independent and identically distributed geometric random variables ($\Gamma_1, \Gamma_2, \dots, \Gamma_n$) where $¶(\Gamma_j=i)=pq^{i-1}$ for $1~\leq~j~\leq~n$ with $p+q=1.$ We study the number of distinct adjacent two letter patterns in such sequences. Initially we directly count the number of distinct pairs in words of short length. Because of the rapid growth of the number of word patterns we change our approach to this problem by obtaining an expression for the expected number of distinct pairs in words of length $n$. We also obtain the asymptotics for the expected number as $n \to \infty$.

The number of distinct adjacent pairs in geometrically distributed words

The Polya urn scheme is a discrete-time process concerning the addition and removal of colored balls. There is a known embedding of it in continuous-time, called the Polya process. We deal with a generalization of this stochastic model, where the initial values and the entries of the transition matrix (corresponding to additions or removals) are not necessarily fixed integer values as in the standard Polya process. In one of the scenarios, we even allow the entries of the matrix to be random variables. As a result, we no longer have a combinatorial model of "balls in an urn," but a broader interpretation as a random walk in a possibly high number of dimensions. In this paper, we study several parametric classes of these generalized continuum Polya-like random walks.

The continuum Pólya-like random walk

Sux trees are one of the most fundamental structures for data compression and pattern matching algorithms. They are retrieval trees (a.k.a. tries) built from the suxes of a string (i.e., a data sequence). A rich combinatorial theory about overlapping strings has been known and utilized for three decades. Some of the combinatorial methods of analysis have been extended, to encompass sux trees built over random strings whose distribution follows a Bernoulli model or a Markov model. Many opportunities exist for an extended, robust theory to much richer stochastic models that are applicable in practice, such as high-order Markov models and Hidden Markov Models. We will survey some recent results about sux trees, derived by analytic, combinatorial, and probabilistic analysis in tandem. We will also outline some challenges for the future analysis of sux

Mark Daniel Ward

Papers

On the Variety of Shapes in Digital Trees

The number of distinct adjacent pairs in geometrically distributed words

The continuum Pólya-like random walk

Sux Trees: A Survey, and Future Challenges