Recent content by Phillips101

About the spoiler; I didn't cover that in my course, I just checked my notes. But, it is fairly 'obvious' when you consider vector spaces, so I suppose I was just supposed to deduce it. And I see the difference now. Thanks for the help, I'll have another go at the problem.

I can't see a difference between our definitions, but yours is certainly clearer. I don't know what that would be. I'd hazard a guess at matrices, but surely that relies on M being free as well?

Take P a free module over an arbitrary ring. Show P is projective. Definition of Projective: If f: M-->N and g: P-->N are module homomorphisms with f surjective, then if P is projective there exists homomorphism h such that h: P-->M with f(h(x))=g(x) for all x. Obviously f has a right...

I've formalised everything and I'm very happy with the answers now - I appreciate all the help

To some_dude, thanks for that clarification. And I haven't had the time to learn any Latex or Tex, but it is high on my to-do list. Thanks for the help

Thanks for the quick reply, and sorry, you're absolutely right the first part of (b) doesn't make sense as there's a typo. I'll make it clearer: (b)X is a compact metric space. F is a closed subset of X, and p is any point of X. Show there is a point q in F such that d(p,q)=infimum(d(p,q'))...

The question I'm doing is as follows: (a) Show that every compact subset of a Hausdorff space is closed. I've done this. (b) F is a compact metric space. F is a closed subset of X, and p is any point of X. Show there is a point q in F such that d(p,q)=infimum(d(p,q')) such that q' is in...

If that's correct, then the thing you posted is distributed as an F distribution, which is what I need? And would swapping beta.hat for beta.hat-beta make any difference to this?

Use the MLE sigma2.hat=(1/n)*||Y-Xbeta.hat||^2 ? This is distributed as a chi-squared n-1 variable if I remember correctly...

Take the linear model Y=X*beta+e, where e~Nn(0, sigma^2 * I), and it has MLE beta.hat First, find the distribution of (beta.hat-beta)' * X'*X * (beta.hat-beta), where t' is t transpose. I think I've done this. I think it's a sigma^2 chi-squared (n-p) distribution. Next, Hence find a...

I have Xi-Xbar ~ N(0, (1+1/n)sigma2) ?

We have X1,...,Xn~N(mu, sigma2) The crux of my problem is finding out the distribution of, say, X1-Xbar (where Xbar is the mean of the n RVs). This is going to end up proving the independence of Xbar and Sxx, btw. I know Xbar~N(mu, sigma2/n), but I don't know how to find the distribution...

Ah! I forgot about that double zero. Very much appreciated

At first glance, your g(z) has an odd number of roots within the disc, whereas f(z) would have an even number (I'm fairly sure of this, since f(z)+1 is even and the first peak's height is greater than 1 - look at a plot of it on wolframalpha or something if you're not convinced). So, I don't...

I believe I have it completely sorted now. Thanks very much, you've been a great help. Sorry if I came across as dim :P