 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability/7/a/i/solution

A partition of a sample space is a finite or countable family of nonempty events such that

B_{i} \cap B_{j} = \emptyset (i \neq = j), i ⋃ B_{i} = Ω.

Thus exactly one event in the family occurs in each outcome. To use ordinary event-conditioned conditional expectations, one usually assumes

P (B_{i}) > 0

; any zero-probability blocks can instead be omitted from the expectation formula.

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