 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2016/s3/2/d/solution

⟨ x ⟩ = 0

. The supplied Gaussian moments give

⟨ x^{2} ⟩_{0} = σ^{2} /2

and

⟨ x^{2} ⟩_{1} = 3 σ^{2} /2

. Therefore

Δ x_{0} = σ / 2, Δ x_{1} = 3/2 σ

. The original plots mark these two symmetric rms intervals around the common mean.

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