VERY HARD Puzzle: What Is The Distance Between Two Random Points In A Square?

by Super User, 1 year ago
0 0
What is the average distance between two randomly chosen points in a square with a side length 1? The video presents how to estimate the answer and also derives the exact answer using integrals. Per suggestions in the comments, I have modified the title to indicate the difficulty level is VERY HARD (a college level calculus course and probability theory course are necessary background).

Blog post


Sources and further reading

Quadruple integral

Difference of two uniform variables

Difference of two uniform variables and solving the double integral

Solving the double integral

Mean distance polar coordinates change

Integral secant cubed

Mean distance square

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Alberto Nishikawa
Brian M. Mooney

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