Using document.head.appendChild() to append a script tag that has an SRC attribute?
element.appendChild
expects a node not a string. You should first create the node and set the attributes and then append it.
element.appendChild Reference
var sc = document.createElement("script");
sc.setAttribute("src", "https://getfirebug.com/firebug-lite.js");
sc.setAttribute("type", "text/javascript");
document.head.appendChild(sc);
For older browsers (IE < 9 etc.) that doesn't support document.head
document.getElementsByTagName("head")[0].appendChild(sc);