This class uses ChatGPT in instruction (in mostly non-essential, education enhancing ways). The following is a light-minded commentary on the tool.

It's well
established now that the way you put a question often
determines not only the answer you'll get, but the type of
answer possible. So ... a mechanical answerer, geared to
produce the ultimate revelations in reference to anything
you want to know, might have unsuspected limitations.

From
Ask A Foolish Question
- by Robert Sheckley

- Sample space, random variables for coin tosses of a biased coin
- Distribution of the sum of two dice
- Distribution of the sum of $n$ dice in "closed" form
- Three levels of expected value theory
- Sum of Bernoulli and normal
- Does pairwise independence imply independence? - very interesting, ChatGPT recovers by itself from initial mistakes, and proves a theorem
- Summary of probability generating functions (pgf)
- Basic t-test
- Summary of moment generating functions and outline of the proof of the Central Limit Theorem - includes commentary on the gaps if we do not use characteristic functions, and highlights the role of Levy" Theorem
- Paired t-test
- Decomposing sample variance, sample size 4, explicitly found iid of standard normals, one of which is the sample mean - We inflicted pain on each other (Chat GPT and I) but the final product has a touch of genius!
- An simple example leading to F-distribution
- Discussion of sample mean as a Minimum Variance Unbiased Estimator (MVUE)

- The Artifice Girl
- An interview with an AI robot -
claim made that
- Chat GPT v.4 is 10 times more intelligent than Chat GPT v. 3.5
- that it has IQ of about 155 (Einstein IQ astimated at 160)
- in 3 years AI will be thousands times more intelligent than an average human

- A darker view of AI