function bg() {

   var imgCount = 3;
   var dir = 'http://local.statamic.com/_themes/img/';
   // I changed your random generator
      //floor: helps getting a random integer
   var randomCount = (Math.floor(Math.random() * imgCount));
   // I changed your array to the literal notation. The literal notation is preferred.
   var images = ['001.png', '002.png', '003.png'];
   // I changed this section to just define the style attribute the best way I know how.
   document.getElementById('banner').setAttribute("style", "background-image: url(" + dir + images[randomCount] + ");background-repeat: no-repeat;background-size: 388px 388px");
}
// Don't forget to run the function instead of just defining it.
bg();