meaning - The use of "random" to mean "arbitrary", "unidentified", "unknown", etc

I'm seeing the use of "random" instead of "arbitrary", etc., with increasing frequency. To me, "random" has a specific meaning and is not synonymous with these other words.
Is it correct to use it in this way?

Answer

The definition of arbitrary does include a link with random:

existing or coming about seemingly at random or by chance or as a capricious and unreasonable act of will.

It is reflected by the usage "at random" (by chance), which is valid.
The problem is, random is with other interpretations of the word "random":

Less widely accepted are a couple of slangy uses of the word, mostly by young people.

• In the first, “random” means “unknown,” “unidentified” as in “some random guy told me at the party that I reminded him of his old girlfriend.”


• The other is to use random to mean “weird,” “strange,” as in “The party at Jessica’s was so random, not what I was expecting at all!”
  Evidently in this expression randomness is being narrowed down to unlikelihood and that is in turn being connected with strangeness, though randomness in real life is usually quite ordinary and boring.

Use of either of these two expressions in formal speech or writing is likely to annoy or confuse your audience.