Any advice? I also have credit for stats 100 should I take stats 107 or 200 as someone with no prior coding knowledge?

Hello. I need help with a practical problem.

There is an unknown total number N of identical items. I hold one item. Once a day, my current item is exchanged for another item chosen at random from the remaining ones (assume uniformly among the other N-1 items). Every day I mark any item I receive with exactly the same mark — I cannot tell individual items apart, only whether the item has been marked before. I keep a log: for each day, whether the item I received was already marked or not.

So my data is a table: day number, and marked/unmarked.

I need a dependence of the form

f1(parameters estimated from the data) = f2(N, probability of N)

i.e. a way to compute, from the observed table, a probability for each possible total number of items N.

As the title says, I could really use some help understanding multivariate fractional logit regressions.

For context, I am working on a project proposal that examines how individuals distribute a fixed number of units/shares across several programs. We originally planned to use a Dirichlet Regression until we realized there is an overabundance of zeros (e.g., people allocating all their shares to one or two programs and none to the others). As an alternative, a multivariate fractional logit regression was proposed, and I am admittedly struggling to understand what this change will mean for the analysis. If someone could explain it in the simplest terms possible, I would greatly appreciate it. If any additional context/information would be helpful, please let me know.

Thank you in advance for any assistance you can offer!

I'm actually really interested in statistics and related fields. I'd love to learn about the different branches of this field and some major international companies that use statistics, so I can research how they apply it in practice.

I'm new to this field and just taking my first steps, so please don't judge me for my question, even if it seems stupid

If I want to estimate what fraction of roulette players betting on red are still ahead after 1,000 spins, is the normal approximation good enough, or does the discreteness matter enough that I should just simulate? Any pitfalls when comparing American (18/38) and European (18/37) wheels?