Lecture Notes

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====== Jonathan Wang  ======

Hi! I'm a fourth year computer science student. Taking Stat 157 and Stat 155 along with Math 104 this semester. I'm also a UGSI for CS 70.

I think this conditional probability question is pretty interesting:
I have two children. One is a boy born on a Thursday. What is the probability I have two boys?

====== Homework  ======

1/18: {{ :math104-s22:s:jonathanwang:hw1.pdf |}}

1/27: {{ :math104-s22:s:jonathanwang:hw2.pdf |}}

2/3: {{ :math104-s22:s:jonathanwang:hw3.pdf |}}

2/10: {{ :math104-s22:s:jonathanwang:hw4.pdf |}}

2/24: {{ :math104-s22:s:jonathanwang:hw5.pdf |}}

3/3: {{ :math104-s22:s:jonathanwang:hw6.pdf |}}

3/10: {{ :math104-s22:s:jonathanwang:hw7.pdf |}}

3/17: {{ :math104-s22:s:jonathanwang:hw8.pdf |}}

4/7: {{ :math104-s22:s:jonathanwang:hw9.pdf |}}

4/14: {{ :math104-s22:s:jonathanwang:hw10.pdf |}}

4/21: {{ :math104-s22:s:jonathanwang:hw11.pdf |}}

====== Questions  ======
1. For 11.2.ii in Ross, why does $s_{n_k}$ need to be greater than $\max\{s_{n_{k-1}}, k\}$ instead of just $s_{n_{k-1}}$?

2. Why is 1(7) in [[https://courses.wikinana.org/_media/math104-f21/math_104-mt1.pdf]] false? I thought one could argue $|a_m - a_n| < \sum \tilde{\epsilon} < \epsilon$

3. Why is 1(9) in [[https://courses.wikinana.org/_media/math104-f21/math_104-mt1.pdf]] false?

4. In Cantor's diagonalization argument, is the reason we can't take the sequence straight downwards because there may be repeated elements?

5. When Prof Zhou showed Cantor's diagonalization argument on 2/15, he produced a monotonically decreasing subsequence. However, I thought in general, although each sequence has a monotonic subsequence, it could be either increasing or decreasing. Thus, was the choice of monotonically decreasing just WLOG?
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