Thread: Sample variance
View Single Post
  #2  
Old November 3rd, 2009, 05:47 PM
matheagle's Avatar
matheagle matheagle is offline
MHF Contributor
  
Join Date: Feb 2009
Posts: 1,957
Country:
Thanks: 127
Thanked 813 Times in 730 Posts
matheagle is a splendid one to beholdmatheagle is a splendid one to beholdmatheagle is a splendid one to beholdmatheagle is a splendid one to beholdmatheagle is a splendid one to beholdmatheagle is a splendid one to beholdmatheagle is a splendid one to beholdmatheagle is a splendid one to behold
Send a message via Yahoo to matheagle
Default
why don't you write down what you've done.

obtain the expectation of...

\sum_{i=1}^n(X_i-\bar X)^2 = \sum_{i=1}^n(X_i-\mu)^2-n(\bar X-\mu)^2

=E\biggl(\sum_{i=1}^n(X_i-\bar X)^2\biggr) = \sum_{i=1}^n V(X_i)-nV(\bar X)

=n\sigma^2-n{\sigma^2\over n} =n\sigma^2-\sigma^2=(n-1)\sigma^2

Next divide by n-1 and it's over
Reply With Quote