Bhisham C. Gupta - Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP

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Introduces basic concepts in probability and statistics to data science students, as well as engineers and scientists Aimed at undergraduate/graduate-level engineering and natural science students, this timely, fully updated edition of a popular book on statistics and probability shows how real-world problems can be solved using statistical concepts. It removes Excel exhibits and replaces them with R software throughout, and updates both MINITAB and JMP software instructions and content. A new chapter discussing data mining—including big data, classification, machine learning, and visualization—is featured. Another new chapter covers cluster analysis methodologies in hierarchical, nonhierarchical, and model based clustering. The book also offers a chapter on Response Surfaces that previously appeared on the book’s companion website.
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.

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The number картинка 582is usually called binomial coefficient , since it appears in the binomial expansion (for integer 345 Example 345 The coefficient of - фото 583)

(3.4.5) Example 345 The coefficient of in the expansion of - фото 584

Example 3.4.5 The coefficient of картинка 585 in the expansion of картинка 586 is since we can write as 346 The coeffic - фото 587 , since we can write as 346 The coefficient of is the number of ways t - фото 588 as

(3.4.6) The coefficient of is the number of ways to pick x of these factors and then - фото 589

The coefficient of картинка 590is the number of ways to pick x of these factors and then choose a from each factor, while taking b from the remaining картинка 591factors.

3.4.4 Arrangements of n Objects Involving Several Kinds of Objects

Suppose that a collection of n objects are such that there are картинка 592's, s s where Then total number of distinguishable arrangements of thes - фото 593's, …, s where Then total number of distinguishable arrangements of these several - фото 594's, where Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 595. Then total number of distinguishable arrangements of these several kinds of A's denoted by Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 596is

(3.4.7) For if we think of each of the n places being originally filled with objects of - фото 597

For if we think of each of the n places being originally filled with objects of type A , there are картинка 598ways of choosing картинка 599's to be replaced by Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 600's. In each of these Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 601ways, there are Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 602ways of choosing картинка 603's to be replaced by картинка 604's. Hence, the number of ways of choosing картинка 605's and replacing them with картинка 606's and choosing картинка 607from the remaining Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 608 A 's and replacing them with Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 609's is Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 610. Continuing this argument and using equation ( 3.4.4) shows that the number of ways of choosing картинка 611's and replacing them with картинка 612's, картинка 613 A 's and replacing them with картинка 614's, and so on until the last A s replaced with s is To illustrate the application of c - фото 615 A 's replaced with s is To illustrate the application of combinations to probability problems - фото 616's, is

To illustrate the application of combinations to probability problems involving - фото 617

To illustrate the application of combinations to probability problems involving finite sample spaces, we consider the following example.

Example 3.4.6(Combinations and probability) If 13 cards are dealt from a thoroughly shuffled deck of 52 ordinary playing cards, the probability of getting five spades is

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