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We create the unit equilateral triangle and put one vertex on each side the of the equilateral triangle and then connect them. What is the expected value of the triangle formed by the connection of these points?

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    $\begingroup$ I suggest asking this on Math StackExchange instead. $\endgroup$
    – user44143
    Commented Sep 7, 2017 at 22:04

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Use barycentric coordinates, as in here. . The formula is just above equation (5), whence the mean follows by indepdence and additivity of expectation (and is equal to $1/4,$ I believe.

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