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Quantitative Trader Interview Questions
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TIQ: A duel is taking place, and the duelists are standing at a distance of x from each other. Each duelist has only one shot. The probability of hitting the target depends on the distance and is represented by the corresponding functions a(x) and b(x) for each duelist. It is known that as they close the distance to x = 0, the probability of hitting for both duelists becomes 1. What strategy should each duelist choose?
TIQ: A plane flies from point a to point b, then immediately flies back in the opposite direction. In which case will the total flight time be longer: when there is a constant wind (for example, blowing from point b to point a) or when there is no wind? Additional Question: What happens if the wind speed is equal to the speed of the plane?
MTQ: Two dice are rolled. Find the probability that the same numbers will appear on both dice. Answers: (0.1235; 0.028; 0.0277; 0.1667; 0.16)
MTQ: A random number generator generates a 5-digit number consisting of 0 and 1. Find the probability that the number generated is 10010. Answers: ( 0.0417; 0.0083; 0.0313; 0.0625; 0.0312)
MTQ: A linear transformation is defined in some basis as Ф = {{2, -1}, {-3, 5}} Find the sum of the components (sum of coordinates) of the point K (2; -6) after linear transformation Ф. Answers: (-11; 5; 10; -26; -18)
MTQ: The area under the graph of the function (between the x-axis and the graph of the function) on the interval from [-a, a] is 24. Find the value of the parameter a. Answers: (2.7774; 2; 1.5; 0.2; 1.7788)
MTQ: Find the value of the fastest increasing function in the point K (-1;1;0). f(x,y,z) = (3x + z^3)^2 + xy + yz + xz + (xy) ^2 / 2. Possible answers: (14; 18; 7; 19; 10)
MTQ: In the tournament in figure skating participate 2 participants from France, 3 participants from South Korea and 4 participants from Germany. Three competitors in the tournament have advanced to the finals. Find the probability that at least two of the finalists are from different countries. ( 0.7714; 0.9524; 0.4286; 0.9405; 0.7143)
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