Correct answer: (C) The MLE always exists but may not be unique.; (D) The MLE consistently estimates μ.
Explanation
Maximizing likelihood minimizes Σ|x_i−μ|. A minimizer is any sample median: unique for odd n (almost surely), and the entire interval between the two middle order statistics for even n. Thus it always exists but can be nonunique. Both middle sample quantiles converge to the unique population median μ; any selection between them is consistent. **C,D**.
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