> BG> I don't know if this "test problem" will clarify things or > confuse them ;-) > > For me, it's confused them. I thought I was following it before, > sorta...
OK, well I'm pressed for time today, so I'll write a nonmathematical version of the problem late tonight or tomorrow or over the weekend. > BG> Consider n rectangles inside the unit square. Call these > rectangles X_1, > BG> X_2,..., X_n > > Are these rectangles at arbitrary locations or all with their origin > at the unit square's origin? Arbitrary locations > BG> Now, we may define some probabilities: > > BG> P(X_i) = the area of the rectangle X_i > > BG> P(X_i | X_j) = (the area of the intersection between the > rectangle X_i and > BG> the rectangle X_j) / (the area of the rectangle X_j) > > So P(X_i | X_j) = how much (from 0 to 1) of X_j is covered by X_i, right? Yes > BG> 1) Choose a large number of points in the unit square > BG> 2) Based on these points, evaluate *some of* the > probabilities P(X_i) and > BG> P(X_i | X_j) > > I don't understand how we get this from the points...are we getting > approximations by selecting arbitrary points and finding out how many > hit X_i and X_j? yes, exactly > Do we know n (how many rectangles total)? yeah... of course if NO relationships involving a given rectangle are given, then you won't even know it exists and can't infer anything about it >Are there some other > relationships involved between these rectangles? All I'm getting out > of this is "we know some rectangles in the unit square, we know some > overlaps, now figure out the rest" but I can't see how what constrains > "the rest" from being completely arbitrary in the given scenario. Figure out the rest of the overlaps between the rectangles you know about (the overlaps you haven't been given) Figure out the areas of any rectangles whose areas you haven't been given And if possible, correct any errors in the given overlaps and areas (errors due to the "points" approximation) I'll write a nonmathematical explanation of the problem later, but I don't have time right now... -- Ben ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/?[EMAIL PROTECTED]
