Download e-book for iPad: A modern introduction to probability and statistics by F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester

By F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester

ISBN-10: 1852338962

ISBN-13: 9781852338961

Likelihood and information are studied via such a lot technology scholars. Many present texts within the zone are only cookbooks and, for this reason, scholars have no idea why they practice the tools they're taught, or why the tools paintings. The energy of this e-book is that it readdresses those shortcomings; through the use of examples, frequently from real-life and utilizing actual information, the authors exhibit how the basics of probabilistic and statistical theories come up intuitively. a contemporary advent to likelihood and information has a variety of fast workouts to provide direct suggestions to scholars. additionally there are over 350 workouts, 1/2 that have solutions, of which part have complete options. an internet site supplies entry to the knowledge documents utilized in the textual content, and, for teachers, the rest recommendations. the one pre-requisite is a primary direction in calculus; the textual content covers general records and chance fabric, and develops past conventional parametric versions to the Poisson procedure, and directly to smooth tools similar to the bootstrap.

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Additional resources for A modern introduction to probability and statistics understanding why and how

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Hence Ω has 4 · 6 = 24 elements. 2 The statement “It is certainly not true that neither John nor Mary is to blame” corresponds to the event (J c ∩ M c )c . The statement “John or Mary is to blame, or both” corresponds to the event J ∪ M . Equivalence now follows from DeMorgan’s laws. 3 In four years we have 365 × 3 + 366 = 1461 days. Hence long months each have a probability 4 × 31/1461 = 124/1461, and short months a probability 120/1461 to occur. Moreover, {Feb} has probability 113/1461. 4 Since there are 7 long months and 8 months with an “r” in their name, we have P(L) = 7/12 and P(R) = 8/12.

4 Calculate P(R3 | R4c ). For more details on the subject of residence time distributions see, for example, the book on reaction engineering by Fogler ([11]). 2 The multiplication rule From the definition of conditional probability we derive a useful rule by multiplying left and right by P(C). The multiplication rule. For any events A and C: P(A ∩ C) = P(A | C) · P(C) . Computing the probability of A ∩ C can hence be decomposed into two parts, computing P(C) and P(A | C) separately, which is often easier than computing P(A ∩ C) directly.

We denote this distribution by Ber (p). Note that we wrote pX instead of p for the probability mass function of X. This was done to emphasize its dependence on X and to avoid possible confusion with the parameter p of the Bernoulli distribution. 46 4 Discrete random variables Consider the (fictitious) situation that you attend, completely unprepared, a multiple-choice exam. It consists of 10 questions, and each question has four alternatives (of which only one is correct). You will pass the exam if you answer six or more questions correctly.

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A modern introduction to probability and statistics understanding why and how by F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester


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