Expected value and variance of random variable

Question

Suppose I pick an integer independently and uniformly at random from $[1,n]$ and I repeat this experiment $t$ times.
Let $a_i$ be the number of times I pick number $i$, and let $a_{max}$ be the maximum $a_i$ of all those chosen in the experiment. Note that $t = a_1+a_2+a_3+...+a_n$

What is the expected value and variance of $\frac{a_{max}}{t}$

So far, I have only been able to relate it to an OEIS entry when $n=2$ http://oeis.org/A230137 — Obinna Okechukwu, Jan 28 '14 at 17:29

score 0 · Answer 1 · edited Apr 13 '17 at 12:20

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This experiment is a well-known experiment called balls-into-bins. As for the expectation, you can find a related question here. Also, you may find these lecture notes useful.

edited Apr 13 '17 at 12:20

Community

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answered Jan 29 '14 at 01:01

Hoda

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Expected value and variance of random variable

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