I'm new to these forums so please forgive me if my question is poorly worded/phrased. Suppose I have a list of N unique integers that I'm drawing from, one at a time, with replacement. Let x be the number of non-repeated integers I've drawn thus far (or, put another way, the number of trials thus far whose outcome was distinct from every trial before it). Finally, let n be the amount of non-repeated integers I'm seeking, n being (obviously) between [0, N]. How many trials will it take, on average, before x=n?
For example, take a deck of cards. If I'm drawing with replacement how many trials will it take until I've seen 26 different cards.