What is the mysterious stranger doing in my vault?

Clicking on him gives you caps.

I got 2460 caps the last time. Others report up to 5000 caps.

Listen for a piano sound. You have a few seconds to find him and get the caps.

He disappears after a second sound is played.

He was added in version 1.2

The mysterious stranger will give you 250 caps if you can tap him before he disappears. He does not appear to take part in combat.

As an addition to other answers.

The important thing about the piano sound is that it is coming from Stranger's location and when playing with headphones and zoomed in at the moment, it is not so difficult to determine the direction and the distance, especially after getting used to it.

The mysterious stranger is a reference to the perk from Fallout 3. Saw him also first time I played after update. Wish he would have hung around little longer though - barely noticed him. Hopefully he shows up next time those f'ng deathclaws do..