 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-1/27k/b/iv/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

Combining the preceding parts,

φ_{X} (u) = e^{- α ∥ u ∥^{2}} .

N (0, 2 α I_{d})

X \sim N (0, 2 α I_{d}) .

When

α = 0

, this means the degenerate distribution concentrated at the origin. This proves the Maxwell characterization of the normal distribution.

 New to topics? Read the docs here!