Correct answer: (A) Converges in distribution to zero; (B) Converges in probability to zero
Explanation
The geometric sum is 10(1−2⁻ⁿ), so λ_n=10·2⁻ⁿ→0. For ε>0, P(X_n>ε)=exp(−ε/λ_n)→0. Thus convergence in probability to zero holds and implies convergence in distribution to zero. **A,B**.
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