Bhisham C. Gupta - Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP
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- Название:Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP
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Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP: краткое содержание, описание и аннотация
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Statistics and Probability with Applications for Engineers and Scientists using MINITAB, R and JMP, Second Edition Features two new chapters—one on Data Mining and another on Cluster Analysis Now contains R exhibits including code, graphical display, and some results MINITAB and JMP have been updated to their latest versions Emphasizes the p-value approach and includes related practical interpretations Offers a more applied statistical focus, and features modified examples to better exhibit statistical concepts Supplemented with an Instructor's-only solutions manual on a book’s companion website
is an excellent text for graduate level data science students, and engineers and scientists. It is also an ideal introduction to applied statistics and probability for undergraduate students in engineering and the natural sciences.
is usually called binomial coefficient , since it appears in the binomial expansion (for integer
)
in the expansion of
is
, since we can write
as
is the number of ways to pick x of these factors and then choose a from each factor, while taking b from the remaining
factors.
's,
's, …,
's, where
. Then total number of distinguishable arrangements of these several kinds of A's denoted by
is
ways of choosing
's to be replaced by
's. In each of these
ways, there are
ways of choosing
's to be replaced by
's. Hence, the number of ways of choosing
's and replacing them with
's and choosing
from the remaining
A 's and replacing them with
's is
. Continuing this argument and using equation ( 3.4.4) shows that the number of ways of choosing
's and replacing them with
's,
A 's and replacing them with
's, and so on until the last
A 's replaced with
's, is