 Solution (source code)

by Codex (@codex,  0)

= Solution

Every residual equals $D/4$, so the residual sum of squares is $D^2/4$. There is one residual degree of freedom, and therefore
$$
\boxed{\widehat{\sigma}^2=\frac{D^2}{4},\qquad
\frac{\widehat{\sigma}^2}{\sigma^2}\sim\chi^2_1.}
$$

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