Probability, calculus & a Square.

You have a square of side-length a. You select two points A and B , "randomly ",anywhere inside the square. The problem is to find the expectation (average) of the length of the straight line segment AB, averaged over all random selections. For a circle , this can be worked out easily, in terms of the radius of the circle. How about , working out the expectation of the distance between two random points inside a square, in terms of its side-length?

Originally posted by ranjan sinha
You have a square of side-length a. You select two points A and B , "randomly ",anywhere inside the square. The problem is to find the expectation (average) of the length of the straight line segment AB, ...[text shortened]... ndom points inside a square, in terms of its side-length?

BTW - what is the expected distance between two randomly chosen points within a circle ? Which , you say , can be worked out
" easily" in terms of the radius of the circle ?

Originally posted by cheskmate
BTW - what is the expected distance between two randomly chosen points within a circle ? Which , you say , can be worked out
" easily" in terms of the radius of the circle ?

Yes , indeed it can be worked out. But that can be the subject matter of another puzzle thread. Off to the new thread then , for it.

Originally posted by ranjan sinha
Yes , indeed it can be worked out. But that can be the subject matter of another puzzle thread. Off to the new thread then , for it.

It look easy BUT Whenn I got down to do it , it turned out that it is not easy at all. May be it can be done numerically by programming the problem and running it on a computer. Analytical solution or expression seems beyond my under-graduate level skills of mathematics.