So I finally found a reference that tells me that the distribution of Z^2 is Chi-squared with df 1. But I didn't find anything that shows me how or why that works.
Will you tell me or point me to somewhere I can see a proof or some explanation? (You must pardon me but I am a math major and like to see how things work.)
Thanks a bunch for your help!
all this is in many books, including walpole.
Use MGFs to prove that the linear combination of normals is normal
and then use that 2-1 transformation to prove that the square of a st normal is a chi-square.
I bet I can find it online.
I can prove it without looking it up, but I want to make dinner and grade exams tonight.
I couldn't find it, but I'll start it for you.
Let z be a st normal and
NOW differentiate wrt x and obtain the realtionship between the two densities and then plug in.
SHOW me your work.
NOW plug in.