Let be a random sample of size 5 from a normal distribution with mean 0 and variance 1, and let
Let be another independent observation from the same distribution
a) What is the distribution of ? I think it's
b) What is the distribution of ?
c) What is the distribution of ?
Oh, the answers I gave were pure guessing, however i hope to know the explantion: I was stuck half way through my working as followed.
b)Find the distribution of .
I actually expanded the question:
since
=
=
=
Applying to my question will yield:
,
then since it was defined initially that , then it should have a distribution of N(0,1) too.
Subsequently, I will have: , where Z is the standard normal. Isn't the equation just cancelled out each other? How does it still remain as ?
Please accept my sincerely apology. Indeed I misread the question as Mr. Fantastic said.
Now it is clear that the question is more interesting than I originally thought. Admittedly, I my self have something to gain by solving it, but I doubt that I could beat you to it.
Thanks, it's a cool solution.
So now I'm interested to know the next distribution:
It seems like it's a F-distribution, but I can't seem to extract the equation to form pattern like
Btw, just curious that for the nominator: , does it convert to ? Then does that mean that will be ??