Research Interview Questions

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“Suppose you have two covariance matrices A and B. Is AB also a covariance matrix? Suppose that, by plain dumb luck, we also have that AB=BA. Is AB a covariance matrix under this additional…”

“3) Poker. 26 red, 26 black. Take one every time, you can choose to guess whether it’s red. You have only one chance. If you are right, you get 1 dollar. What’s the strategy? And what’s the expected…”

“2) A. 10 ropes, each one has one red end and one blue end. Each time, take out a red and a blue end, make them together. Repeat 10 times. The expectation of the number of loops.

B. 10 ropes, no…”

“Suppose you have 100 GB of data that you want to sort, but you only have 1 GB of memory. How would you sort this data?”

“A tosses n+1 coins. B tosses n coins. B wins if he has at least as many heads as A. What is the probability that B wins?”

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“If X, Y and Z are three random variables such that X and Y have a correlation of 0.9, and Y and Z have correlation of 0.8, what are the minimum and maximum correlation that X and Z can have?”

“1) Tow coins, P(head)=1/3, P(tail)=2/3, design a way to get the effect of fair coin”

“V~U[0,1]. Make a bet B, for V, and will be awarded 1,5 times V if B>V, otherwise your bet is worthless - you do not lose anything as well. What is your bet?”

“5 babies in a room, 2 boys and 3 girls. one baby with unknown sex is added. Randomly choose one baby and the result is a boy. What's the prob that the added baby is a boy?”

“There is a game where you have three coins, and your opponent has three coins. You both flip your coins at the same time. If the number of heads you have matches the number of heads he has, then you…”

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