exercises for Week 3, 3 February to 9 February

This week we have proved a lemma relating convergence in probability and convergence almost surely, and used this to prove the continuous mapping theorem for convergence in probability. We have proved the Portmanteau theorem, and (almost) proved that any of the statements of that theorem are equivalent with the c.d.f. definition of convergence in distribution. See Ex. 2.19(e) in the errata to the book. We have also proved the continuous mapping theorem for convergence in distribution. Next week we'll get to the Cramer--Slutsky rules, and then introduce the notion of tightness. 

This week you may try Exercises~2.9, 2.11, 2.12, 2.13, 2.15, 2.16, and 2.19(e). For 2.19(e), see the errata in stk4090errata.pdf