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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 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?

13 Answers

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?

12 Answers

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

12 Answers

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

13 Answers

How many numbers between 1 and 1000 contain a 3?

13 Answers

You have two decks of cards: a 52 card deck (26 black, 26 red) and a 26 card deck (13 black, 13 red). You randomly draw two cards and win if both are the same color. Which deck would you prefer? What if the 26 card deck was randomly drawn from the 52 card deck? Which deck would you prefer then?

11 Answers

Drawing a pair of (x, y) from a joint Gaussian distribution with 0 covariance. Knowing the stndard deviations of x and y and knowing z = x + y, what is your best guess for x?

10 Answers

What is the probability of breaking a stick into 3 pieces and forming a triangle?

8 Answers
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