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Quantitative researcher Interview Questions

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What's the best unbiased estimator for a series random variables?

5 Answers

I guess it is just a Gaussian distribution (Normal dist.). Since it has the smallest uncertainty (from quantum point of view) or variance.

I guess it is just a Gaussian distribution (Normal dist.), since it has the smallest uncertainty (from quantum point of view) or variance.

It is the OLS estimator (with Gauss-Markov approximations and normality), by Fisher's theorem on Maximum Likelihood Estimators.

You observe a sample of measurements coming from a fixed length ruler. If the object is shorter than the ruler you observe the actual measurement. Otherwise you observe the length of the ruler. What would be a good estimator of the ruler length?

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How to measure 9 minutes using only a 4 minute and 7 minute hourglass

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You have 2 decks of cards (each deck contains both red and black cards). One deck has twice the number of cards in the other deck with the same color ration (so one deck has 52 cards and the other has 104, both half red and half black). I offer you to play a game. First you get to chose which deck of cards you want to play with. Second, you draw 2 cards at random from your deck of choice. If both are red, then I will give you a ferarri. Which deck of cards would you chose?

13 Answers

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 earn?

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N points lie on a circle. You draw lines connecting all the points to each other. These lines divide up the circle into a number of regions. How many regions is this? Assume that the points are scattered in such a way as to give the maximum number of regions for that N.

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The first question he gave me was not hard. 1. You call to someone's house and asked if they have two children. The answer happens to be yes. Then you ask if one of their children is a boy. The answer happens to be yes again. What's the probability that the second child is a boy? 2. (Much harder) You call to someone's house and asked if they have two children. The answer happens to be yes. Then you ask if one of their children's name a William. The answer happens to be yes again.(We assume William is a boy's name, and that it's possible that both children are Williams) What's the probability that the second child is a boy?

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Given log X ~ N(0,1). Compute the expectation of X.

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If we flip a coin 100 times, what is the probability of getting even number of heads?

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How many numbers between 1 and 1000 contain a 3?

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