The 5th talk within Seminar series in Statistics and Data Science of this semester, will take place at Erling Svedrups plass (Niels Henrik Abel Hus, 8th floor), on Tuesday 02.11.2021 at 14:15. The talk will be given by Nils Lid Hjort, a Professor at the Department of Mathematics, University of Oslo.

Access to the seminar area physically at this point is not planned to be restricted. Yet, it will be possible to follow the talk on Zoom, using this link:
https://uio.zoom.us/j/63196215431?pwd=cjd5WWFGeDZXaXFHa1VXK0w4T3VCUT09

Title:
How many draws until we’ve seen all cards? And how many different cards are there?

Abstract:
Cards are drawn, one at a time, with replacement, from a deck of n cards. I study the total time $W_n$ needed until we have seen all n cards, via different perspectives, along with a Gumbel limiting distribution.Various non-trivial identities, involving different perspectives for moments and Laplace transformations, are found as corollaries. These findings are also used to estimate the number of different cards, if uknown. If I needed to sample 133 words from a document, before I had 50 different words, what is the vocabulary size for the document? How many words did Shakespeare know (including those he never used in his writing)?

An Abels Tårn podcast about some of these themes, which attracted a fair amount of inspired comments and guesses from the public (specifically, finding the mean of $W_n$ above, for the case of $n = 52$ cards), can be found on the Abels Tårn website, July 2021, as a conversation with Torkild Jemterud, Jo Røislien, and myself.

Best regards,
Sven Ove Samuelsen & Aliaksandr Hubin