 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-4/26k/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Assume

X_{n} \to X

L^{2}

. The reverse triangle inequality for the

L^{2}

norm gives

∣ ∥ X_{n} ∥_{2} - ∥ X ∥_{2} ∣ \leq ∥ X_{n} - X ∥_{2} ⟶ 0.

Squaring the norms yields

E [X_{n}^{2}] ⟶ E [X^{2}] .

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