STAT400: Midterm Review

I think it would also be helpful to review how to find an inverse CDF, since I’m still a bit unsure about that.

Could we also go over approaches for finding the \(c\) constant for the envelope in the accept-reject method?

Lastly, going over the accept-reject method and Monte Carlo sampling would be great!

What are some ways to come up with an envelope when the uniform does not work?

What are some good ways to prove that the envelope is valid?

I am really confused about the method of using envelopes. I don’t really understand how to use them, nor why or when we would want to use them.

I would like you to cover how to create the best ‘envelope’ for accept-reject method. And please provide an example, I noticed in our notes we don’t really have a defined envelope in the examples provided; I just want to see the thinking process on how to create the envelope.

I would like to request that we go over envelope functions a bit more, and I am struggling a bit to understand specifically what they are and how they are found.

Could we go over a specific example and/or a review of finding the Var(g(x)) using a Monte Carlo approach?

I was wondering if, when we are using methods 1 & 2 for Monte Carlo Integration, is the uniform distribution the only distribution we can use? In other words, if the uniform distribution isn’t a good option, is method 3 our go-to? If not, how would we use other distributions in that way?

In our review on Tuesday, would you elaborate more on why Monte Carlo integration is superior to approximating an integral via the sum of polygons? I know that we talked about how the estimate produced by Monte Carlo converges towards the true value of the integral as m increases, but I don’t quite understand why this is better than increasing the number of polygons, especially because Monte Carlo inherently involves randomness.

Also, from Homework 3, we had to do integration by parts; could we go over a similar example during Tuesday’s review?

Going over marginal densities and trying a new example that isn’t the drive-up and walk-up window one used from notes.

Could we review some examples using group_by, summarise, filter (etc.) like we did earlier in the semester?

I was wondering if it would be possible to elaborate on what we can expect from the coding-based questions on the exam.