Probability Theory
Anton, 21.01. 14:30-15:00
- 1. Define conditional expectation
- 2. What if F is trivial?
- 3. What if X and F are independent? Prove it.
- 4. Example 3.3.
- 5. What can you tell me about the conditional expectation if X is in L2? (Thm 3.6) Prove it.
- 6. Martingale convergence: State the Theorem. Give an example of a Martingale that converges P-a.s. but not in L1. I stated example 3.11.3.). He wanted me to show why I Sn converges P-a.s. to infinity. I wasn't able.
- 6. What do we need for the proof of the martingale convergence? ( Upcrossing)State the inequality? How do we prove it? (idea).
So, Sznitmans exam is pretty special. My best advice would be to learn to state any statement as quickly as possible. He tries to put you in pressure as much and as quickly as he can. I wasn't prepared for it. You almost cannot take 5 seconds to think without hearing " You HAVE to know this!", " We did this numerous times!" or "Come on, that's supposed to be easy!". Personally, I knew this was going to come, but I underestimated how hard it is to concentrate in these circumstances. I therefore failed to answer some questions (or state easy facts) and for others, he just said that this was too much time. He will tell you if he wants you to prove anything. My Fazit: Learn the statements as good and precisely as you can. He got pretty angry when I forgot to say that a RV had to be integrable for the second time. But all in all he is fair and - I think- aware of how he puts you in a difficult (but instructive) position.
