Introduction to Probability“Donald claims that he won the popular vote if you subtract the 3 million illegal voters. Assuming that 3 million people did vote illegally, compute the probability that Donald is correct.”

**Text: **Introduction to Probability by David F. Anderson, Timo Seppalainen, and Benedek Valko

**Prof:** Dr. Martin Lohmann

Dr. Lohmann’s lectures largely consisted of (usually) interesting examples. Some students found his accent and his handwriting a bit challenging to follow. This, combined with the fact that he defers posting of lecture notes, made the course harder than necessary for such students. I did not have any difficulty understanding what was being said, and the few times I found his handwriting became hard to read, he clarified immediately. Also, if you ask a stupid question, expect some deft sarcasm in response!

**Difficulty**

While I find probability counter-intuitive, the assignments were all quite doable. Occasionally, harder questions marked with a star were provided. The first midterm was quite tricky, however, we were given a practice midterm beforehand that was conceptually quite similar to the actual exam. The second midterm and final were both significantly easier and we also were given similar practice material.

**Key Concepts**

Counting

Sets

Discrete vs Continuous Probability Distributions

Mean, Variance and Covariance

Joint Distribution

Convergence in Probability/Distribution

Conditional Probability

Moment-generating functions

** Hard Concepts**

Counting: I always make incorrect assumptions w/regard to counting. I think the key to easier problems is to identify whether you are using replacement/no replacement and order/no order. For harder problems, it is often necessary to construct a bijection of sorts or use a symmetry argument.

**Conclusion**

Good to get some practice with counting and probability. About as much theory as you would expect from such a class.