I am in a Stats class and honestly don't know whats going on. Ironically, I am considerably better off then everyone else in my class.
We have a set of problems that no one knows where to even start. I was hoping some people here can give me a hand and help me out with them. Thanks in advance. Finals week sure is rough in college!
A) Let Xi 1 â?¤ i â?¤ n be iid with mean Âµ and variance Ï?^2
Deï¬?ne the sample variance by S^2 = (1/nâ??1) (Sigma i=1 to n) (Xi-Xbar)^2.
Show that E[S ^2 ] = Ï?^2
B) Suppose X and Y are independent and V ar(X) = 1, V ar(Y ) = 4. Find
appropriate weights w1, w2 â?¥ 0 satisfying (w1)^4 + (w2)^4 = 1 to maximize the variance of
(w1)X + (w2)Y
Thanks again for the help. Any advice is greatly appreciated.