 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-4/13k/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The OLS normal equation with an intercept gives

\hat{β} = S_{X Y} / S_{XX}

. By the law of large numbers it tends to

Cov (X, Y) / Var X

. Here

X = Z + U + ϵ_{X}

and

Y = X + U + ϵ_{Y}

, so the limit is

(3 + 1) /3 = 4/3

, showing upward confounding bias.

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