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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Referring to the statement in Theorem 3.3.1 that картинка 505and Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 506are disjoint events whose union is S , we have the following rule.

Theorem 3.3.2(General rule of complementation) If Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 507 are events in a sample space S, then we have

(3.3.5) Another useful result follows readily from 332c by mathematical induction - фото 508

Another useful result follows readily from (3.3.2c) by mathematical induction

Theorem 3.3.3(Rule of addition of probabilities for mutually exclusive events) If Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 509 are disjoint events in a sample space S, then

(3.3.6) Example 332Determination of probabilities of some events Suppose that a - фото 510

Example 3.3.2(Determination of probabilities of some events) Suppose that a nickel and a dime are tossed, with H and T denoting head and tail for the nickel and h and t denoting head and tail for the dime. The sample space S consists of the four elements Hh, Ht, Th, and Tt. If these four elements are all assigned equal probabilities and if E is the event of getting exactly one head, then Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 511, and we have that

Now suppose that and are arbitrary events in S Then from Figure - фото 512

Now suppose that картинка 513and картинка 514are arbitrary events in S . Then from Figure 3.2.2, with and it can be easily seen that are three disjoint events whose union is - фото 515and it can be easily seen that are three disjoint events whose union is That - фото 516, it can be easily seen that are three disjoint events whose union is That is 337 - фото 517, are three disjoint events whose union is That is 337 Also and - фото 518. That is,

(3.3.7) Also and are disjoint sets whose union is - фото 519

Also, картинка 520and are disjoint sets whose union is Hence 338 Similarly - фото 521are disjoint sets whose union is Hence 338 Similarly 339 Solving - фото 522. Hence,

(3.3.8) Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 523

Similarly

(3.3.9) Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 524

Solving ( 3.3.8) for Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 525and ( 3.3.9) for Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 526and substituting in ( 3.3.7), we obtain the following.

Theorem 3.3.4(Rule for addition of probabilities for two arbitrary events) If картинка 527 and are any two events in a sample space S then 3310 The rule for three - фото 528 are any two events in a sample space S , then

(3.3.10) Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 529

The rule for three events Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 530is given by

(3.3.11) Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 531

More generally, for n events Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 532, we have,

(3.3.12) Note that for if and - фото 533

Note that for картинка 534, if Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 535and Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 536are disjoint, Statistics and Probability with Applications for Engineers and Scientists Using MINITAB R and JMP - изображение 537and ( 3.3.10) reduces to ( 3.3.6); that is,

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