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A robot encounters a bunch of coins spread out on the ground. It examines each coin and, if the coin is heads, turns it to tails with 100% probability. If the coin is tails, it turns it to heads with 50% probability. He examines each coin once per cycle. If you have the robot cycle through the coins a very large number of times, what will eventually happen to the proportion of heads and the proportion of tails?
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Trading Analyst Intern

Interviewed at DRW

4.3
Jan 29, 2014

A robot encounters a bunch of coins spread out on the ground. It examines each coin and, if the coin is heads, turns it to tails with 100% probability. If the coin is tails, it turns it to heads with 50% probability. He examines each coin once per cycle. If you have the robot cycle through the coins a very large number of times, what will eventually happen to the proportion of heads and the proportion of tails?

Go to a bar, throw darts for 500 times, 1/2 probability hitting the target, 1 point awarded for each hit. Now getting drunk and throw for 500 times, 1/2 probability hitting the target but 3 points award now. (1) What is the expected score/number of hits? (2) If we got 1100 points, give a feasible (say 15 points) interval estimate of points? (3) How to make this calculations exact?
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Quantitative Intern

Interviewed at Jane Street

4.4
Oct 8, 2013

Go to a bar, throw darts for 500 times, 1/2 probability hitting the target, 1 point awarded for each hit. Now getting drunk and throw for 500 times, 1/2 probability hitting the target but 3 points award now. (1) What is the expected score/number of hits? (2) If we got 1100 points, give a feasible (say 15 points) interval estimate of points? (3) How to make this calculations exact?

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