[caseyryan]

package {
         public class RandomPositioner extends Sprite {
                   private var _image:Bitmap = new Bitmap(new BitmapData(100, 100, 0xff0000, false));
                   public function RandomPositioner() {
                          if (stage) init();
                          else addEventListener(Event.ADDED_TO_STAGE, init);
                   }
                   private function init(e:Event = null):void {
                           setRandomPosition();
                   }
                   private function setRandomPosition():void {
                           if (stage == null) return;
                           _image.x = stage.stageWidth * Math.random();
                           _image.y = stage.stageHeight * Math.random();
                   } 
         }
}

что-то типа того