- 09 Jan '05 09:02 / 3 editsYou 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?
- 10 Jan '05 07:41 / 1 edit

BTW - what is the expected distance between two randomly chosen points within a circle ? Which , you say , can be worked out*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?**

" easily" in terms of the radius of the circle ? - 12 Jan '05 11:35

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 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 ? - 16 Jan '05 12:51 / 1 edit

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.*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.**