A return to Problems of the Week.
So I’ve been quite quiet on the blogging front recently. But, having recently recovered from one of those pesky travel-related illnesses (which I was vaccinated for back in Australia; it seems the vaccine didn’t work too well) I am now back and saying hello to anyone reading this again.
Last night a neat little mathematics problem entered my head, so I’ve decided to post it up here. But before I get to that, I’ll also include a quick English problem:
Should the title of this post be “Problems of the Weeks”? I mean, one problem of the week is simply the Problem of the Week. If I had many problems, all in the same week, then they would be Problems of the Week. But, as is the case here, where I have multiple problems spread out over multiple weeks, what is the correct grammatical description?
Now that the English-nerds have something to keep them occupied, I’ll move on to the much more entertaining mathematics problem.
Suppose I am collecting basketball cards. There are n cards in the set, and every time I purchase a card I have an equal chance (1 in n) of receiving any particular card. The first time I get a double (ie receive a card that I already have a copy of) is when I receive my 50th card. What is the most likely (integer) value for n?
Stated another way, the problem is this: Positive integers between 1 and n inclusive are uniformly randomly generated with replacement. The first time a number is generated that has already been generated is on the 50th generation. What is the MLE (maximum likelihood estimate) for n?
Good luck! I have no idea what the answer is myself, I haven’t stopped to think about it yet. This weekend I am heading off to Los Angeles for a week’s worth of holidays (woohoo!) so I’ll try to provide an answer by the end of that. Cheers.
Last night a neat little mathematics problem entered my head, so I’ve decided to post it up here. But before I get to that, I’ll also include a quick English problem:
Should the title of this post be “Problems of the Weeks”? I mean, one problem of the week is simply the Problem of the Week. If I had many problems, all in the same week, then they would be Problems of the Week. But, as is the case here, where I have multiple problems spread out over multiple weeks, what is the correct grammatical description?
Now that the English-nerds have something to keep them occupied, I’ll move on to the much more entertaining mathematics problem.
Suppose I am collecting basketball cards. There are n cards in the set, and every time I purchase a card I have an equal chance (1 in n) of receiving any particular card. The first time I get a double (ie receive a card that I already have a copy of) is when I receive my 50th card. What is the most likely (integer) value for n?
Stated another way, the problem is this: Positive integers between 1 and n inclusive are uniformly randomly generated with replacement. The first time a number is generated that has already been generated is on the 50th generation. What is the MLE (maximum likelihood estimate) for n?
Good luck! I have no idea what the answer is myself, I haven’t stopped to think about it yet. This weekend I am heading off to Los Angeles for a week’s worth of holidays (woohoo!) so I’ll try to provide an answer by the end of that. Cheers.