Correct answer: (A) Convergence in distribution to a real constant c implies convergence in probability to c.
Explanation
For A,apply distribution convergence at c−ε and c+ε to show P(|X_n−c|>ε)→0. B fails for rare large spikes. Marginal convergence alone does not determine the joint dependence required by C. D fails with centered iid nondegenerate variables whose means all equal zero. **A**.
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