Midterm 1 Q&A

1 General math

1.1 When simplifying a sum, how do you know when to reindex?

Reindexing a sum is analogous to applying a \(u\)-substitution to an integral, so a lot of your intuitions about that carry over. But to be concrete, let me draw your attention to some examples from the course where a reindex happened:

  • Problem Set 0 #2;
  • Prob

In each case, the form of the original expression tips you off about

Do whatever you have to do to muscle it into that form.

2 Set theory and probability spaces

2.1 How do you start proofs?

3 Counting

3.1 How do you tell if order matters or not?

3.2 Under what circumstances do the “ordered” and the “unordered” answers agree?

We saw this on the Spotify.

3.3 I am confused about “stars and bars.”

4 Conditional probability

5 Independence

6 Discrete random variables