Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

Problem: Let {Xn},{Yn} - real-valued random variables.

{Xn}-->{X} - weakly; {Yn}-->{Y} weakly.

Assume that Xn and Yn - independent for all n and that X and Y - are independent.

Fact that {Xn+Yn}-->{X+Y} weakly, can be shown using characteristic functions and Levy's theorem.

Question:

If independence does not hold, can you construct a counterexample?

I appreciate any help in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Weak convergence of the sum of dependent variables, question

Loading...

Similar Threads for Weak convergence dependent |
---|

A About the “Axiom of Dependent Choice” |

I Determining functional relation of two dependant variables |

B Conditional Probability, Independence, and Dependence |

I Independent versus dependent pdf |

**Physics Forums | Science Articles, Homework Help, Discussion**