 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2017/prelims/mathematics-iii/7/a/ii/solution

For

0 \leq t \leq 1

P (\frac{M}{θ} \leq t) = P (X_{1} \leq θt, \dots, X_{n} \leq θt) = t^{n} .

F_{M / θ} (t) = ⎩ ⎨ ⎧ 0, t^{n}, 1, t < 0, 0 \leq t \leq 1, t > 1.

It contains no

θ

, so

M / θ

 New to topics? Read the docs here!