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3 votes
1 answer
180 views

A question about average deviation of given $n$ complex numbers

This question just came to my mind and I have no idea as to how to approach it. Let $z_1,z_2,\dots,z_n$ be $n$ be any complex numbers in the unit disc $|z| \leq 1.$ Consider a complex function on the …
6 votes
2 answers
487 views

Average distance of the mean of $n$ random complex numbers in a unit disc

Let $z_1,z_2,\dots,z_n$ be $n$ complex numbers distributed uniformly and randomly over the unit disc $x^2+y^2 \leq 1$. Let $z$ be the complex number defined by the mean of the of these numbers,that i …
8 votes
3 answers
1k views

Taking points uniformly inside a general finite geometric domain

It is well known that if we want to take $n$ uniformly and randomly points inside a circle of radius $r$ and centered at the origin the following apparently correct approach for generating $x$ and …