A mean that doesn't exist

Hello everyone, I've came across this problem and I need to see if my approach is right...

An urn initially contains one Black and one White ball. At each stage, a ball is randomly chosen and then replaced along with another of the same color. Let denote the selection number of the 1st Black ball chosen.

(a)Find the pdf of .

(b)Show that the doesn't exist for .

for (a), I thought that if I came accross a black ball I'll replace it so

and for any .

As for (b), which is 2!!

How could this be?!

Any help is very much appreciated!