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Quantitative research analyst Interview Questions

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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?

17 Answers

My initial answer was to use the MAX of the sample. That however is a biased estimator. How can you account for the bias and come up with an unbiased estimator? I think this is where you need to start making assumptions on the distribution. A uniform distribution would allow to estimate the bias.

what kind of distribution is it? what do we do with the data? what precision should we get? what happens if we "lose" the oversize data?

I came up a solution: if we know the distribution of actual measurement and the value of actual measurement, then the expected probability of getting wrong measurement should equal to the probability of actual measurement greater than length of ruler. Not sure this is correct and will interview on friday. good luck to me.

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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?

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.

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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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Imagine I flip 100 coins in a sequence, and you need to guess the sequence. You are allowed to ask one yes/no question. What do you ask to maximize the probability of guessing the sequence?

9 Answers

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?

8 Answers
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