## STAT430 : HomeworkTwo

Referers: Fall2007 :: OldNews2007 :: (Remote :: Orphans :: Tree )
Dorman Wiki
Dorman Lab Wiki

1(a) 7 pts
(b) 7 pts
(c) 7 pts
(d) 7 pts
2(a) 7 pts
(b) 7 pts
(c) 7 pts
3(a) 6 pts (6 pts bonus for thinking independently)
(b) *bonus* 7 pts
(c) 7 pts
4(a) 7 pts
(b) 13 pts
(c) 7 pts
(d) 7 pts
Total: 96 pts with opportunity for 109 pts with *bonus*.  There is really no logic to the totals here; it's a consequence of deciding these things at 3am.

##### 0Questions
• I have a question about question 4 in HW2. Is the result that we are to show in part a) supposed to be "Covariance(U,V) = variance(X) * sum(aij) * sum(brj)" or is it correctly written as "Covariance(U,V) = variance(X) * sum(aij*brj)"? -Ryan Babbitt
The result is correctly written.  Recall $X j$ are independent.
• Where to start?
I think the problem is interpretation of the request "3(a) Derive the pdf of X."  You are told that the distribution of $S 2 _ Z σ 2 _ Z S 2 _ Y σ 2 _ Y$ BY DEFINITION is called an F distribution.  You are also given the pdf of this distribution called F.  When asked "Derive the pdf of $X ∼ F$" it means prove why the given pdf results for $S 2 _ Z σ 2 _ Z S 2 _ Y σ 2 _ Y$ (equations in this sentence are messed up, but see your notes for the statistic involving sample variances and population variances from two independent normal samples).  One such proof is given in the handouts on this wiki.  If you use this proof, please make it your own by writing it up independently and justifying the steps.  Another way to the solution that should better work your thinking muscles is to follow an approach similar to the one used to derive the t-distribution in class.