October 2008
Intermediate to advanced
984 pages
30h 43m
English
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Appendix A. Hints from Probability and Statistics
A.1. Total Probability and the Bayes Rule
Let Ai, i = 1, 2,…, M, be M events so that ∑Mi = 1P(Ai) = 1 P(Ai) = 1. Then the probability of an arbitrary event B is given by(A.1)
where P(B|A) denotes the conditional probability of B assuming A, which is defined as(A.2)
and P(B, A) is the joint probability of the two events. Equation (A.1) is known as the total probability theorem. From the definition in (A.2) the Bayes rule is readily available(A.3)These are easily extended to random variables or vectors ...
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