Robert P. Dobrow - Probability
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Probability: краткое содержание, описание и аннотация
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distinguished researchers Drs. Robert Dobrow and Amy Wagaman deliver a thorough introduction to the foundations of probability theory. The book includes a host of chapter exercises, examples in R with included code, and well-explained solutions. With new and improved discussions on reproducibility for random numbers and how to set seeds in R, and organizational changes, the new edition will be of use to anyone taking their first probability course within a mathematics, statistics, engineering, or data science program.
New exercises and supplemental materials support more engagement with R, and include new code samples to accompany examples in a variety of chapters and sections that didn’t include them in the first edition.
The new edition also includes for the first time:
A thorough discussion of reproducibility in the context of generating random numbers Revised sections and exercises on conditioning, and a renewed description of specifying PMFs and PDFs Substantial organizational changes to improve the flow of the material Additional descriptions and supplemental examples to the bivariate sections to assist students with a limited understanding of calculus Perfect for upper-level undergraduate students in a first course on probability theory, is also ideal for researchers seeking to learn probability from the ground up or those self-studying probability for the purpose of taking advanced coursework or preparing for actuarial exams.
people. Each person in the subset turns over his/her card, from 0 to 1. The cards taken from left to right form a new binary list. For instance, if
and the first and third persons are selected, the corresponding list is
.
th position in the list, then person
is selected. If the list is
, then all but the second person are selected.
and binary lists of length
. Table 1.3shows the correspondence for the case
.
-element set is equal to the number of binary lists of length
. The number of binary lists of length
is easily counted by the multiplication principle. As there are two choices for each element of the list, there are
binary lists. The number of subsets of an
-element set immediately follows as
.















with exactly
ones. We will do so by first counting the number of
-element subsets of an
-element set. In the subset-list correspondence, observe that every
-element subset of
corresponds to a binary list with
ones. And conversely, every binary list with exactly
ones corresponds to a
-element subset. This is true for each
. For instance, in the case
and
, the subsets are