Question: 1. Convergence. a) Prove that CLT implies the weak LLN. d Hint: Use the fact that if c is a constant and Xn c,

1. Convergence. a) Prove that CLT implies the weak LLN. d Hint:

1. Convergence. a) Prove that CLT implies the weak LLN. d Hint: Use the fact that if c is a constant and Xn c, then Xn c d d b) Construct a counterexample where X X and Y Y, but X + Y does not converge n n in distribution to X+ Y.

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