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.

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