Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Discrete mathematics, continuous mathematics and probability / 7 / a / iii

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- Solution iii

Solution

Mutual independence means that for every nonempty

I \subseteq {1, 2, 3}

,

P (i \in I ⋂ A_{i}) = i \in I \prod P (A_{i}) .

Beyond the trivial single-event identities, this requires the three pairwise equalities and the triple equality

P (A_{1} \cap A_{2} \cap A_{3}) = P (A_{1}) P (A_{2}) P (A_{3})

. Pairwise independence alone omits that last requirement.

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