There're k balls in a bag, each one with a different colour. Draw one ball from the bag randomly each time, then put the ball back.
Let random variable X = the number of balls to draw until all k colours have been seen. Find E(X).
Please help me with this question, thanks!
This is the "coupon collector's problem". As the Wikipdia article explains, the expected value is $k$ times the $k$th harmonic number: $$ k\left( 1 + \frac 1 2 + \frac 1 3 + \cdots + \frac 1 k \right). $$