If two independent variables X and Y are uncorrelated then
Options:
(A) Cov
(B) Cov
(C) Cov
(D) −1 < Cov
Official Answer Key:
A
Step-by-Step Solution & Explanation
By definition, Cov(X,Y) = E[XY] − E[X]E[Y]. For independent (hence uncorrelated) variables, E[XY] = E[X]E[Y], so Cov(X,Y) = 0 identically — it is neither necessarily positive, negative, nor merely bounded between −1 and 1 (that bound applies to the correlation *coefficient*, not the covariance itself). Answer: (A).
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