Non-Uniform Coupon Collector’s Problem

The Coupon Collector’s Problem is a neat little problem in probability, and I first heard about it recently on the statistics subreddit. You, like me, might be familiar with it if you’ve ever tried to solve the expected number of boxes of cereal to buy to get all the toys. Not that I have that problem right now, but it shows up on probability quizzes and the like.

The problem’s solution hinges on two things. One, there is replacement (sampling from a seemingly infinite population of items that are in some proportion). Two, all items are equally likely. What happens when they aren’t equally likely? We turn back to Absorbing Markov Chains (AMC), because apparently that has to be 50% of what I talk about on here!

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