Wednesday 11 July 2012

Differences in Area

Find the expected difference in area of a rectangle and a square whose length, breadth and side are chosen uniformly randomly from an interval of (0,1)?

2 comments:

  1. Expected Area of a Rectangle = xy dx dy = 1/4

    Expected Area of a Square = a^2 da = 1/3

    Therefore, required difference = 1/12

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    Replies
    1. There are integrals from 0 to 1, over x, y and a.

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