why don't you write down what you've done.
obtain the expectation of...
Next divide by n-1 and it's over
This is a proof question that I just cannot get what's required for the life of me. This isn't part of my assessed homework, just fyi.
Suppose , , ..., is a random sample from a random variable which has expectation and variance . Consider the sample variance
Show that
We're also given the hint that may be written as and that . I've used both of these but I just can't seem to get at all. Closest I've gotten is
Proving this fact is equivalent to proving . First, it's worth stating for clarity that, with respect to the summations, the term is a constant, so we can move it in and out of summations as we wish. Expand the quadratic and distribute the sum across the terms, which will give you . Now, note that and , which allows us to simplify our expression further to (the term n(ybar) is NOT in the sum). Now we use the linearity of the expectation operator to get . The expectation of a square is the variance plus the square of the mean (you can get this by rearranging the formula for the variance), so use that to evaluate each of the expectations to get . This, of course, will simplify to , completing the proof.
Thankyou! I think it was this key fact that I was missing...I was sat thinking "this must be something but couldn't fathom what. Cheers
I've gotten wrong for doing that in the past. Something about this site's not for checking work. + it would've taken me ages to type out what I'd done.