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Brainteasers
1. a normal dice with 6 sides with numbers from 1 to 6, toss it at most
three time. After each toss, you get a number x, you can either continue or
get x dollars. What is the game worth?
2. the same rule as question 1, What would you like to pay to play the game?
3. a coin, toss a number times until you get a head, say N. You will get
paid with 2^N, what is the game worth?
4. The same rule as question 2, what would you like to pay to play the game?
5. three pieces of pizzas, 1 with both sides burned, 1 with 1 side burned, 1
with 0 side burned. Stack them together blindly, you see the top surface is
burned, what is the probabilty for the other side of the top pizza being
burned?
6. a normal dice, two players, X and Y. X starts tossing the coin first, if
a
6 is shown, the game stops and X wins, otherwise, Y tosses and so on. What
is the probability for x to win?
7. A pile of 1000 stones, split it to two piles x and y, you get a number xy
. Split x and y further, you a number for each of them. repeat the process
until there are 1000 piles of 1 stone, add all the numbers together, what is
the sum? Why do you always get the same answer even your splitting is
arbitrary?
8. A string of length 1, cut it to two strings of length x and y, you get a
number xy. Then you do similar splitting and add all the numbers up. what is
the limit of the sum?
9. couples shaking hands, forget details, please google.
10. answer this question in 10 sec: a ball with a radius 2 weighs 80 ouces,
how much does a ball with a radius 3 weigh?
11. There are 100 statements, the nth statement says: among the 100
statement, at most (n-1) are true. How may are true?
math
1. what is the distance from the origin to the surface 2x+3y+4z=12?
2. what is i^i
3. If x is a gaussian variable N(0,1), what is E{x^n}
4. What is type I and II errors? what is the power of test? Central limit
theorem, estimator theory.
5. what makes a valid correlation matrix?
6. how to generate correlated random walk series?
7. What schemes to solve PDEs?
8. What is Quasi-random number and why?
9. do you know how to find minimum value of a function?
10. what is monte carlo simulation/integration?
11. 50
C++/algorithm
what is virtual function/inheritance, public/private/protected member/
inheritance, static member/function, dynamic/static cast, template?
STL quesitons: how to use sort, map? How to implement map idea with vector?
what is an initializatoin list and in what situation such an list must be
provided
what is design pattern, any examples?
how to sort an array? the order of complexity.
how to define a tree and vist all elements of the tree?
finance
1. an vanilla bond has a positive convexity, what security may have a
negative convexity?
2. what is the distribution of correlation coefficient of two random stocks
like?
3. how many stocks should be appropriate in a portfolio?
4. how to ensure that your portfolio has a 60% probability of having a
return >10%
5. time-series: what is ar/ma/arch/garch, why? how to test non-constant
volatility
behavioal
Give an example to illustrate how to deal with deadline/bad collaborator/bad
project/mistake and so on.
answers or hints
Brainteasers
1. work backwards, like an american option, get asked about this question
serveral times, this seems a must-ask question for interviewers.
2. if you are risk-neutral, you get the same answer as in 1, not otherwise.
3. Infinity
4. if you are risk-neutral, you get the same answer as in 3, not otherwise.
5. 2/3
6. 6/11
7. 1000*999/2
8. 1/2, use geometrical method, xy is like area of a square.
10. 270 ouces
math
1. get the normal vector to the surface or minimize x^2+y^2+z^2
2. write the base i as e^(2N*Pi+1/2*pi)
3. use moment-generating function and do taylor expansion
4. consult a statistics book.
5. symmetrical semi-definit
6. Chelosky decomposition or diagnalization
7-10 see numerical recipe
C++/algorithm
All C++ questions can be answered by reading Stroustrup's book except design
pattern, for which you need google
sort: know at least 3 sorting algorthm and say how it works
tree: pre-order, post-order
finance
1. callable bond
2. positive skewed
3. ~200? not sure
4. no idea
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