How many N in [100,400] s.t. N^N is perfect square
Data Researcher Interview Questions
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Maximizing Sharpe ratio related question
Suppose you are given a cube, you break the cube in 3X3X3 pieces. However, before doing so, all 6 faces of the cube were colored green. All the other faces not colored green will be white after breaking it up. You randomly pick a small cube and see one face which is green. What is the probability that the cube is an edge cube?
You have a total of 4 investments to make of 100 dollars. You can either invest in a stock which if it goes up in value, you gain an additional 100 dollars, if it goes down, you lose 50 dollars. Or you can bet on whether the stock will go up or down at the casino, where you either win 100 if you're right or lose everything if not. Can you devise a strategy where you will always make a profit?
A game where two players each throw two dice each. If any one die matches the other, you win a dollar. If there is no match, you lose a dollar. Would you play this game or not and why?
1a) A bus runs on a loop. It takes to the bus 10min to complete the loop. You go to the bus stop at random times, what's the expected time you'll be waiting for the bus? 1b) Along the way the bus driver stops for 10 min with a 50% chance. For how long you wait now? 2) There's a rounded table, you wanna place three legs randomly, what's the chance the table stands?
Expected length of the longest segment of a unit-length stick broken in 2 places.
What is the probability that three random points on a unit circle would form a triangle that includes the center of the unit circle?
Some sample questions: Q. You have a biased coin in which the probability of getting a head is 51%. Create an event out of this coin which has a probability of 25%. Q. There is a calculator in which all digits (0 to 9) and the basic arithmetic operators (+, -, *, /) are disabled. However other scientific functions are operational like exp, log, sin, cos, arc tan, etc. The calculator currently displays a 0. Convert this first to 2 and then to 3. Q. There are five points in an equilateral triangle of side length 1. Prove that there are two points with distance less than 1/2.
Let's play another game: There are 100 balls, you and I pick the balls in turn, for each round you can pick 2^k balls(k=0,1,2,...). Do you have a strategy to win?
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