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- dirtydroog
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[job interview] Two uniforms on [0,1]
Do you guys have to solve these while the interviewers are looking at you, or they leave you alone in the interview room, or you get to do them at home?Just out of curiosity!
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- rimaephosie
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[job interview] Two uniforms on [0,1]
while the interviewer is looking at you
[job interview] Two uniforms on [0,1]
QuoteOriginally posted by: rimaephosieHi, This is a job interview teaser :Consider two iid uniform r.v. on [0,1] .Let's and Calculate .Unfortunately, don't have a paper and a pen with me, but the first thing that comes into my mind is 1) Use the following cheap trick:2) Remember that after allSo it should just break down into integration of several linear functions over several 2-dimensional regions.
[job interview] Two uniforms on [0,1]
QuoteOriginally posted by: rimaephosiewhile the interviewer is looking at you and grinning in an unsettling manner
Last edited by samyonez on July 23rd, 2007, 10:00 pm, edited 1 time in total.
[job interview] Two uniforms on [0,1]
I did this problem using the basic integration approach.Let two RV be x and y. For x<y the problem can be reduced to three cases,1) x > y-x and x > 1-y and x<y2) y-x > x and y-x > 1-y and x<y3) 1-y > x and 1-y > y-x and x<ySolve each set of three constraints and you will get 11/108 as the expected value for each cases. That makes it 33/108 for x<y case.By symmetry, 33/108 for y<x. So the final number is 66/108=11/18.
[job interview] Two uniforms on [0,1]
this question looks like an intermediate calculation for the problem of a stick broken uniformely into 3 pieces and eventualy forming a triangle. is that correct?If it is, this is not the correct method to solve this puzzle
[job interview] Two uniforms on [0,1]
It is related, but not quiet. We can think of U(1), U(2)-U(1), and 1-U(2), as the lengths of the three pieces of the stick. Now, max{U(1), U(2)-U(1), 1-U(2)} is nothing but the length of the longest piece, which can range from 1/3 to 1. Note that it is not necessary for the three pieces to form sides of a triangle (that is a different problem). This problem can be solved very elegantly by conditioning on the length of the longest piece.
[job interview] Two uniforms on [0,1]
Can somebody give a clue how to obtain the general solution, instead of putting the final result? Thanks a lot...
[job interview] Two uniforms on [0,1]
I found a nice reference on problem like this:On the Lenghs of the Pieces of a Stick Broken at RandomBy Lars Holst, Journal of Applied Probability, Vol17, 1980