Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-2/26k/b/solution

Saying that has law means that is the pushforward measure
For a real random variable, is a probability measure on .
The pair consists of independent random variables when
for every pair of Borel sets ; equivalently, their joint law is the product of their marginal laws.

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