Conditional Probability

A few facts concerning conditional probability needed in Chapter 3 are reviewed here. For further details, consult Chapters 6 and 7 of the book by Ross [99].

Let *A* and *B* denote events in a sample space *S*. The conditional probability of *A* given *B*, written prob(*A*|*B*), is defined by

(D.1)

where *AB* is the joint event of *A* and *B*. When prob(*A*|*B*) = prob(*A*), we say that *A* and *B* are independent.

As an example, suppose that *X* and *Y* are discrete random variables taking on non-negative integer values. If *A* is the event “*X* = *k*” and *B* is “*Y* = *i*,” then (D.1) becomes

Let *B _{i}* be a collection of disjoint events indexed by

*i*whose ...

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