Separating the four modes of convergence
ProofIntermediate⏱ 30 minProbabilityconvergencecounterexample
Problem
Construct random variables demonstrating each of the following, and prove your constructions work.
- but not almost surely.
- almost surely but not in .
- but does not converge to in probability.
Write a complete argument. Every inequality you use should be one you could state precisely.
Hints
Hints — 0 of 3 revealed
Solution
Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.
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