By E. Jolivet (auth.), Didier Dacunha-Castelle, Bernard Van Cutsem (eds.)
ISBN-10: 3540086587
ISBN-13: 9783540086581
Read or Download Journées de Statistique des Processus Stochastiques: Proceedings, Grenoble, Juin 1977 PDF
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Extra resources for Journées de Statistique des Processus Stochastiques: Proceedings, Grenoble, Juin 1977
Example text
8), P {B} P {A | B} = P {A} P {B | A} . 33 (Situation on a midterm exam). On a midterm exam, students X, Y , and Z forgot to sign their papers. 5, respectively. After the grading, he notices that two unsigned exams are good and one is bad. Given this information, and assuming that students worked independently of each other, what is the probability that the bad exam belongs to student Z? Solution. Denote good and bad exams by G and B. Also, let GGB denote two good and one bad exams, XG denote the event “student X wrote a good exam,” etc.
It is used every time when it is easier to compute conditional probabilities of A given additional information. Consider some partition of the sample space Ω with mutually exclusive and exhaustive events B1 , . . , Bk . It means that Bi ∩ Bj = ∅ for any i = j and B1 ∪ . . ∪ Bk = Ω. These events also partition the event A, A = (A ∩ B1 ) ∪ . . 6). Hence, k P {A} = and we arrive to the following rule. 34 (Reliability of a test, continued). 32. 04. 99. 7983. 35 (Diagnostics of computer codes). A new computer program consists of two modules.
Summary and conclusions . . . . . . . . . . . . . . . . . . . . . Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 10 11 13 14 15 18 20 20 22 27 32 33 This chapter introduces the key concept of probability, its fundamental rules and properties, and discusses most basic methods of computing probabilities of various events. 1 Events and their probabilities The concept of probability perfectly agrees with our intuition.
Journées de Statistique des Processus Stochastiques: Proceedings, Grenoble, Juin 1977 by E. Jolivet (auth.), Didier Dacunha-Castelle, Bernard Van Cutsem (eds.)
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