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Date: 14-3-2021
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Let and be sets. Conditional probability requires that
(1) |
where denotes intersection ("and"), and also that
(2) |
Therefore,
(3) |
Now, let
(4) |
so is an event in and for , then
(5) |
(6) |
But this can be written
(7) |
so
(8) |
(Papoulis 1984, pp. 38-39).
REFERENCES:
Papoulis, A. "Bayes' Theorem in Statistics" and "Bayes' Theorem in Statistics (Reexamined)." §3-5 and 4-4 in Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 38-39, 78-81, and 112-114, 1984.
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 810, 1992.
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دراسة يابانية لتقليل مخاطر أمراض المواليد منخفضي الوزن
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اكتشاف أكبر مرجان في العالم قبالة سواحل جزر سليمان
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اتحاد كليات الطب الملكية البريطانية يشيد بالمستوى العلمي لطلبة جامعة العميد وبيئتها التعليمية
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