Sollicitatievraag bij Susquehanna International Group

Programming questions: What is the difference between Python 2.7 and Python 3. What does "yeld" keyword do in Python. How to rename a file in Linux terminal. Math problems: Q1. You and I toss a fair coin 3 times each. What is the probability that you and me will have equal number of heads? Q2. There are two kids, they want to go to movies. In order to decide whether they go to movies we give a coin to each kid and lock them in separate rooms. Then we ask each kid to come out and either bring a coin or leave the coin in the room. (1) If nobody brings a coin - they both don't go to cinema. (2) If only one kid brings a coin we toss it: head - both go to movies, tail - nobody goes to movies. (3) Both bring a coin - we toss each coin. If there are 2 heads - both go to movies , otherwise nobody goes. What is the probability that both kids will go to movies if they choose the optimal strategy. Kids can not communicate nor before or after being separated into rooms. Q3. There are three random variables: X, Y, Z. We know that Corr(X,Y)=0.9, Corr(X,Z)=0.9, Corr(Y,Z)=0.6. Is there anything wrong? Q4. Find average value of the function f(x,y,z)=3*x-4*y+5*z over the triangle (simplex) x+y+z=1 (0<x,y,z<1). Q5. A is a matrix, A*A=0. What does it mean (1) for eigenvalues of matrix A, (2) for rank of A (put a constraint on rank of A)? Q6. There are three horses 1,2,3. You pay 1$ to make a bet. If the horse "1" wins you get 2$ back, if horse "2" - 4$ back, if horse "3" - 6$ back. How would you make your bet? Hint: the game is fair, the prices (payoffs) are chosen rationally.