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I wonder how it predicts download time..

When sending header and getting response, it may be able to time response but without downloading the file (or take a predefined speed rate), it is impossible to measure download time, or it could be pretty inaccurate.

For FF user, download statusbar is an option, but it shows information in the status bar while downloading the file.

Well most of us use some kind of Download Manager, but getting file size before starting downloading file looks difficult, No workaround
for FF users

Search for Firefox addon with name “get file size firefox” in google. I am sure you will found something useful.