An Introduction to Probability Theory by P. A. Moran

By P. A. Moran

Книга An advent to chance thought An advent to likelihood idea Книги Математика Автор: P. A. Moran Год издания: 1984 Формат: pdf Издат.:Oxford college Press, united states Страниц: 550 Размер: 21,2 ISBN: 0198532423 Язык: Английский0 (голосов: zero) Оценка:"This vintage textual content and reference introduces chance idea for either complicated undergraduate scholars of data and scientists in similar fields, drawing on actual purposes within the actual and organic sciences. "The ebook makes chance exciting." --Journal of the yank Statistical organization

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8) shows how, for given events F1 , F2 , . . , Fn of which one and only one must occur, we can compute P (E) by first “conditioning” upon which one of the Fi occurs. That is, it states that P (E) is equal to a weighted average of P (E|Fi ), each term being weighted by the probability of the event on which it is conditioned. Suppose now that E has occurred and we are interested in determining which one of the Fj also occurred. 9) is known as Bayes’ formula. 15 You know that a certain letter is equally likely to be in any one of three different folders.

What is the probability that the coin landed tails? *45. An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn c additional balls of the same color are put in with it. Now suppose that we draw another ball. Show that the probability that the first ball drawn was black given that the second ball drawn was red is b/(b + r + c). 46. Three prisoners are informed by their jailer that one of them has been chosen at random to be executed, and the other two are to be freed.

They continue tossing the dice back and forth until one of them wins. What are their respective probabilities of winning? 15. Argue that E = EF ∪ EF c , E ∪ F = E ∪ F E c . 16. Use Exercise 15 to show that P (E ∪ F ) = P (E) + P (F ) − P (EF ). *17. Suppose each of three persons tosses a coin. If the outcome of one of the tosses differs from the other outcomes, then the game ends. If not, then the persons start over and retoss their coins. Assuming fair coins, what is the probability that the game will end with the first round of tosses?

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