Welcome to the second discussion! This time we have some set of problems based on what’s been said in class lately. You can check the book too if you are stuck or just ask me later or during. Let’s begin!
Problem 1
Given $X \sim N(0,1)$, what is the best way to find out the distribution of $X^2$? Do you have any guesses?
Problem 2
Bob eats candy every hour. He sometimes eats lolly pops, fruit, and chocolate bars. If we don’t know how Bob will pick, is it fine to model his choices with a continuous or discrete distribution? Why do you think so?
Problem 3
Suppose someone did a regression of $X$ on $Y$. Just because a linear fit was possible within chance and the error was small, does it mean that $X$ and $Y$ are linearly related? How could you tell? Do you ever truly know and why is it that you can’t? As an extra, someone proposes the measure
\[\vert \vert \vec{y} - \vec{x} \vert \vert_2\]to assess error. He asks for your opinion, what’s your take? Do you like it?
Last one!
Mary is collecting crabs for a dna inspection, landfill use has polluted their waters. Jill is studying the effects of diet and exercise among overweight 40 year olds. How might the data between Mary and Jill differ? How does the task they have at hand change the way they interpret their data, tools, and report?
Have a great rest of your day!
(These are just sample questions, you can make your own discussions, they are left here as an illustration).