 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2012/m/m2/a/solution

f (x, y) \geq 0 almost everywhere, \int_{R^{2}} f (x, y) d x d y = 1.

It determines the joint law by

Pr ((X, Y) \in B) = \int_{B} f (x, y) d x d y

B

. Values on sets of planar measure zero may be changed without changing that law.

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