Problems from the book 'All of Statistics':
Note: these are my own solutions to problems for which there exist a solution to cross reference elsewhere online, see the curriculum for links to definitive solutions.
Chapter 1: Probability
- Chapter 1 problem 1
- Chapter 1 problem 4
- Chapter 1 problem 5
- Chapter 1 problem 6
- Chapter 1 problem 7
- Chapter 1 problem 9
- Math Monk Independence
Chapter 2: Random Variables
- Chapter 2 problem 4
- CDF proof
- Chapter 2 problem 8
- Chapter 2 problem 9
- Uniform X, Y problem
- Uniform triangle joint density problem
- Chapter 2 problem 20—transforming uniform $f_{X,Y}$ with $X-Y$ and $X/Y$
- Chapter 2 problem 21—computing max of IID exponential RVs
- Binomial in terms of 2 Poisson
- CDF of transformation of unit disk (TODO)
- Independence of RVs associated with coin flips
- Independence of functions of random variables (TODO)
Chapter 3: Expectation
- Expectation and variance of a Binomial random variable
- Expectation and variance of a Geometric random variable
- Expectation and variance of a Poisson random variable (TODO)
- Expectation and variance of exponential transformation of Normal RV (TODO)
- Conditional Expectation of Uniform of Uniform
- Variance of linear combinations of random variables
- Reasoning about RVs that are 1 when Uniform RV is within bounds (TODO)
- Chapter 3 problem 2—Variance is zero iff RV has a point mass distribution
- Chapter 3 problem 3: Expectation and Variance of max of Uniform RVs (TODO)
- Chapter 3 problem 7 (TODO)
Chapter 4: Inequalities
- Sub-Gaussian inequality (TODO)
- Finding bounds with Hoeffding’s inequality and Bernstein’s inequality (TODO)
Chapter 5: Convergence of Random Variables
To transcribe and do: