Z_n is the average of iid Bernoulli indicators with success probability F_X(x), so it is unbiased and has variance F_X(x)(1−F_X(x))/n, not n². The law of large numbers gives consistency. The covariance is [F_X(min(x,y))−F_X(x)F_X(y)]/n, generally nonzero. **A,D**.
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