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.

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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

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Aufgaben und Lehrsätze aus der Analysis

We consider a randomized selection algorithm that has n initial participants and a moderator. In each round of the process, each participant and the moderator throw a biased coin. Only the participants who throw the same result as the moderator stay in the game for subsequent rounds. With probability 1, all participants are eliminated in finitely many rounds. We let Mn denote the number of participants remaining in the game in the last nontrivial round. This simple algorithm has surprisingly many interesting applications. In particular, it models (asymptotically) the number of longest prefixes in the Lempel–Ziv ’77 data compression scheme. Such multiplicity was used recently in [13] to design an error-resilient LZ’77 scheme. We give precise asymptotic characteristics of the jth factorial moment of Mn for all j ∈ N. Also, we present a detailed asymptotic description of the exponential generating function for Mn. In particular, we exhibit periodic fluctuation in the distribution of Mn, and we prove that no limiting distribution exists (however, we observe that the asymptotic distribution follows the logarithmic series distribution plus some fluctuations). The results we develop are proved by probabilistic and analytical techniques of the analysis of algorithms. In particular, we utilize recurrence relations, analytical poissonization and depoissonization, the Mellin transform, and complex analysis.

Analysis of Randomized Selection Algorithm Motivated by the LZ'77 Scheme.

Data Science is one of the newest interdisciplinary areas. It is transforming our lives unexpectedly fast. This transformation is also happening in our learning styles and practicing habits. We adv...

Fostering Undergraduate Data Science

Many modern networks grow from blocks. We study the probabilistic behavior of parameters of a blocks tree, which models several kinds of networks. It grows from building blocks that are themselves rooted trees. We investigate the number of leaves, depth of nodes, total path length, and height of such trees. We use methods from the theory of Pólya urns and martingales.

https://www.stat.purdue.edu/~mdw/papers/paper024.pdf

Building random trees from blocks

Research on learning communities has primarily focused on identifying institutional outcomes such as student achievement and retention. However, more research is needed on how the learning community experience impacts the motivation, beliefs, and perceptions associated with student success. This study investigates the psychosocial effects of participating in a residential research-oriented learning community regarding students’ interest and motivation in pursuing research-oriented careers, research and data self-efficacy beliefs, sense of belongingness with the learning community, and socialization levels and career awareness in research-oriented fields. This study also investigated the mediating effects of students’ initial research self-efficacy beliefs on differential gains regarding career awareness, motivation and interest, and sense of belongingness and socialization after one year of participating in a residential research-oriented learning community. Participants of the study consisted of five cohorts of the learning community, each composed of twenty students. Students in each cohort participated in a pretest-posttest design survey study. Findings suggest that alignment of student interest with the learning community discipline is a key mediator of student growth in their self-efficacy beliefs, sense of belongingness with the learning community and levels of socialization, and career awareness in the selected field. Implications include recommendations for the thoughtful design of learning communities that promote cognitive apprenticeships by orchestrating the content, method, sequencing, and sociology of the learning environment.

Characterizing the psychosocial effects of participating in a year-long residential research-oriented learning community

The devastating effect of errors in adaptive data compression is a long-standing open problem. In this paper LZ'77 is changed theoretically and experimentally observed, such that in a significant proportion of LZ'77 phrases, there is more than one copy of the longest prefix in the compressed file. Once the redundant bits of LZ'77 have been identified, it is exploited for channel coding. For error correction and detection RS (255,255-2e) Reed-Solomon codes are used.

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Mark Daniel Ward

Papers

Analysis of Randomized Selection Algorithm Motivated by the LZ'77 Scheme.

Fostering Undergraduate Data Science

Building random trees from blocks

Characterizing the psychosocial effects of participating in a year-long residential research-oriented learning community

Error resilient LZ'77 scheme and its analysis