Seymour Lipschutz, John J. Schiller's Schaum's Outline of Introduction to Probability and PDF

By Seymour Lipschutz, John J. Schiller

ISBN-10: 0070380848

ISBN-13: 9780070380844

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Extra resources for Schaum's Outline of Introduction to Probability and Statistics (Schaum's Outlines Series)

Sample text

Am E Am . 8 may easily be extended, by induction, to the product of m sets; that is, n(Al x A 2 x ... x Am) = n(Al )n(A2 ) . . 8 CLASSES OF SETS, POWER SETS, PARTlTlONS Given a set S, we may wish to talk about some of its subsets. Thus we would be considering a "set of sets". Whenever such a situation arises, to avoid confusion, we will speak of a class of sets or a collection of sets. If we wish to consider some of the sets in a given class of sets, then we will use the term subclass or subcollection.

Remark 1: It is common practice in mathematics to put a vertical line " I " or slanted line "j" through a symbol to indicate the opposite or negative meaning of the symbol. Remark 2: The statement A <;;; B does not exclude the possibility that A = B. In fact, for any set A, we have A <;;; A since, trivially, every element in A belongs to A. However, if A <;;; B and A el B, then we say that A is a proper subset of A (sometimes written A e B) . Specifying Sets There are essentially two ways to specify a particular set.

LO Thus micrometer A is more precise. 18. Estimate the correlation coefficient for each data set shown in the scatterplots in Fig. 31. r The correlation coefficient r lies in the interval [- 1 , 1 ] . Moreover, r is close to 1 if the data are approximately linear with positive slope, r is close to -1 if the data are approximately linear with negative slope, and r is close to O if there is no relationship between the points. Accordingly: (a) r is close to 1, say r 0. 9 , since there appears to be a strong linear relationship between the points with positive slope.

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Schaum's Outline of Introduction to Probability and Statistics (Schaum's Outlines Series) by Seymour Lipschutz, John J. Schiller


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