Time to get to know your friendly χ²ₙ random variable. The density function is pretty messy, and best understood after learning about the Gamma RV (take Math 181A!), so here we’ll simply use R to generate values from χ²ₙ using rchisq from the d-p-q-r quartet. Let X ∼ χ²ₙ and Y ∼ χ²ₘ where X and Y are independent.
Consider these three questions:
1) What is E(X)?
2) What is SD(X)?
3) What RV is X+Y?
For each question, write some code that helps you make a guess. Include your code and your conjecture. (Obviously, one could cheat and Google the answers to these questions, but I hope you will not do so given how few opportunities you get in school to form conjectures. Explore and enjoy, as real scholars do.)