1. sigma_A = 0.2, sigma_B = 0.3 and correlation = 0.5. Find the portfolio that has the lowest portfolio sigma.
Ans: 6/7 of A and 1/7 of B
2. Each cereal box contains a piece of toy. There are 4 kinds in total. What is the expected number of boxes you have to buy in order to get the entire collection?
Ans: 8.33333
3. What is the expected number of toss in order to get 3 consecutive H from a fair coin?
Ans: 1 H takes 2 tosses; 2 H's takes 6 tosses; 3 H's takes 14 tosses; n H's takes 2^(n+1)-2 tosses. See Zhou, under Markov chain, for details.
4. There are n people in the room, everyone has shaken hand with everyone else. If there are totally 66 handshakes, what is n?
Ans: 12
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