This seems like a typical Bayes' Rule question, but I'm having trouble formulating it properly.
Say I'm a speaker on a conference tour which moves from city to city. I'm trying to estimate how many people will attend my talk in the next city, given how many attended in previous cities.
For example, say the total number of attendees in each city is 100, and that there are five simultaneous, equally likely tracks, so I start in the first city assuming that 20 people will attend (i.e., my first prior is 0.2). In actuality, 30 people attend. How do I use that evidence to predict how many will attend in the next city? How about the one after that?
It feels like I ought to be able to write a simple Bayes' Rule expression for this, but everything I try seems wrong. Any help would be appreciated.