The diagonal of a quadrilateral
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I'll leave the computation via R to you. The are distributed uniformly on the intervals
, so that
each with mean/expectation
and variance
We have
so that
Now,
and
We have
because and
are independent when
, and so
giving a variance of
and so the standard deviation is
# # #
A faster way, assuming you know the variance of a linear combination of independent random variables, is to compute
and since the are independent, each covariance is 0. Then
and take the square root to get the standard deviation.