T Nation

Statistics Help


Hey guys,

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 µ 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.


That shit looks boring^^


This was my approach to #2. I assumed they were 0 mean. Thats one fucker of a problem.

Clean up the first one as I think that one is much easier.


That boring shit saves lives


I hate my business stats class. I'd help you but I only allocate my brain to think stats one night a week from 630-9Pm.


Thanks for the reply. Quick question- on the 3rd line of the right page did you forget a square root?

Here is the first one fixed up. I'm surprised these notations aren't printable:

Let Xi 1(less then or = to) I (less then or = to) n be iid with mean µ and variance (Sigma^2)
Define the sample variance by S^2 = (1/ n minus 1]) (Sum i=1 to n) (Xi-Xbar)^2.
Show that E[S ^2 ] = Sigma^2


Yes I did forget that square root. Was the zero mean assumption correct?


I'll find out today. Any chance you can work around with that other one? I have a few more if you've got some free time. Want me to message you later?

Thanks again for your help. You're a life saver.


I played with it but I'm not happy with the way it came out.

I know how to do it though, and I think you should do a double sum in the E{S^2}. Sum(i = 1:N) Sum(j = 1:N) x_i * x_j sort of thing. When i = equals j, you will get N times sigma^2, then the rest of the times, N^2-N you will get the second moment. I was using xbar as the sample mean, and I had to go through and calculate its mean, variance, and second moment which was a pain in the ass.

What class is this for?


70% of statistics are made up... so just make up every answer and you're bound to get at least a C. Its science


How about you post on a math forum?

Not saying we don't have smart folks here, but that a good forum might help you out during finals week.


its impossible to decipher part A, as is - repost with proper formatting


Ok, got it. Looks like you're given the sample variance (s^2) and then asked to show how it accurately approximates the population variance (lowercase sigma^2) - for sure this explanation is in your textbook and in one of the early chapters too. Hope that helps


Bullshit. Powerlifting saves lives.