probability - Coupon Collector's Problem -- Expected Value of each item

So I guess my problem is based on the famous coupon collector's problem, which is, if you should not be familiar with it, the following:

Given N different coupons from which coupons are being drawn independantly, with equal probability and with replacement: How many coupons do you expect to need to draw before having drawn each coupon at least once? (Wikipedia has a well written article about it).

My problem is the following: I need to know what is the expected value for each coupon after we have collected at least one copy of each coupon.

More formal: We label each of the N coupons with numbers 1,...,n. Let $X_i$ be a random variable which counts how often we have drawn coupon $i$. What is $\mathbb{E}[X_i]$?

Answer

The expected value of the number of purchases until you have obtained the complete collection is $E_n=\sum\limits_{i=1}^{n}\frac{n}{n-i+1}=n\sum\limits_{k=1}^{n}\frac1k$. For reasons of symmetry $E(X_i)=\frac{E_n}{n}=\sum\limits_{k=1}^{n}\frac1k$ for all $i$.