Bootstrap-related issue

Say I re-sample $N$ items with replacement from a numbered item sample of size $N$. What is the average number of data items that are not selected in each such sampling?

Hint: what is the probability that a specific item is not sampled in $1$ draw? what is the probability that it is not sampled in $N$ draws? Now use the linearity of expectation.
• If you could elaborate... the probability that a specific item is not sampled in $N$ draws is $[(N-1)/N]^N$.
• @Omri: so the average number you would expect not to be sampled at all is $N\left( \frac {N-1}N \right)^N$. Feb 12, 2013 at 21:43
• Thanks! Interestingly, the average portion of $N$ that is not sampled approaches $1/e$ as $N$ goes to infinity...