Correct answer: (C) Cov(S_n(x),S_n(y))=F(x)(1−F(y))/n for all real x,y and n≥2.
Explanation
The general covariance formula is [F(min(x,y))−F(x)F(y)]/n. C’s expression is valid for x≤y,but is asserted for all x,y,and is false when the order reverses. Thus the official answer is **C**. A is Glivenko–Cantelli and B follows from the Bernoulli CLT and Slutsky. D also has a printed issue:the square inside the supremum makes it a two-sided Kolmogorov statistic,whose limit is not χ²₂ even for continuous F. A one-sided unsquared supremum,then squared,would have the claimed χ²₂ scaling under a continuous null. Official grading is retained.
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