Javascript - File Upload Not Working In Firefox

I have in my asp.net page

<input id="MyTextBox" runat="server" type="text" name="T1" size="20"/>
<asp:Button ID="UploadFileButton" runat="server" Text="Upload" />
<input id="FileUpload" runat="server" type="file" style="height: 22px; visibility:hidden;" />

linked to js script:

$("#UploadFileButton").live("click", function(event) {
event.preventDefault();
$("#FileUpload").click();
});
$(function() {
$('#FileUpload').change(function() {
$("#MyTextBox").val($(this).val());
});
});

this means when the user click UploadFileButton ,the chose file select popup shows.After the user chose a file the MyTextBox=Selct file path.

My problem is that my script works in Chrome but not in firefox.