Say we have a piece of length one, and then we draw twice from a bin of sticks in which there are an infinite amount of sticks with lengths evenly distributed on $[0,1]$. In cases where a triangle can be formed, what is the expected area of the formed triangle?
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1$\begingroup$ en.wikipedia.org/wiki/Heron%27s_formula $\endgroup$– domotorpOct 18, 2017 at 18:51
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3$\begingroup$ This is the wrong forum for your question, which essentially asks for the value of a (n iterated) definite integral (Heron's formula for the integrand) over a simply described domain. Gerhard "Web Search May Be Faster" Paseman, 2017.10.18. $\endgroup$– Gerhard PasemanOct 18, 2017 at 18:55
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$\begingroup$ Some double integrals are nontrivial . . . this one might even be a K3 period. Are you sure you know how to evaluate the integral that arises here? (cf. mathoverflow.net/questions/206352) $\endgroup$– Noam D. ElkiesOct 19, 2017 at 2:26
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$\begingroup$ It may be impossible to solve the integral exactly. However, the question as posed does not shed light on what has been tried or assumed. You might turn it into a good question with a good answer, but let's see something more from the original poster. Gerhard "For Example, What's My Motivation?" Paseman, 2017.10.18. $\endgroup$– Gerhard PasemanOct 19, 2017 at 2:45
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$\begingroup$ Seems to be a natural enough question that "motivation" isn't really needed, but yes, it would still be nice to have some indication of what if anything the original poster tried. $\endgroup$– Noam D. ElkiesOct 19, 2017 at 3:17
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