Recent content by longrob

Thanks for your reply. That's what i thought. So I assume the easiest/typical way is the way I described above ?

Hi all I am looking for a simple way to show that the mean of the Cauchy distribution us undefined. This is because this integral diverges: \underset{-\infty}{\overset{\infty}{\int}}\frac{x}{x^{2}+a^{2}}dx Now, I know one proof which replaces the limits of integration with -x1 and x2. After...

OK, here goes again. I think I fixed the LaTex problems: let \mathbf{A=X^{\textrm{T}}X} where \mathbf{A} is a n\times n square symmetric matrix with elements a_{ij}. \mathbf{\mathbf{\boldsymbol{\beta}}} is the n\times 1 column vector. Expanding out...

Hi Fredrik Thanks so much for the explanation ! So, just to be clear if I put begin{align} end{align} around the text from Lyx, it should solve the problem ? Thanks again LR

Hi all I use Lyx v1.65 for creating LaTex. Obviously it displays OK in Lyx. It also displays OK with an online editor I've tried http://www.codecogs.com/latex/eqneditor.php But invariably when I try to post LaTex to this forum it does not work. I've tried the sandbox which the reason...

Hi again I need to stick with the pure linear algebraic derivation at the moment, but thanks anyway. I may come back to you later on that, as I am also interested in the geometric interpretation. Anyway, I think I have solved it. Basically, it revolves around the "rule" that the derivative...

Hi Bacle, thanks for your messages. I'm glad I'm not the only one who is a bit confused by it. For completeness and the benefit of others, I'll explain the setup so that it's not necessary to refer to the link I posted. We have y = XB + e where y is a n x 1 column vector of responses X is a...

Excuse me: I meant "the 3rd term in the expression above" not "the 2nd term on the RHS".

Hi and thanks for your reply. Could you take a look here: http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf On page 18/19 you see exactly what (I think) you are referring to in terms of the orthogonal projection. What I am referring to is on the bottom of page 19: "Differentiating with...

Hi all In the derivation of the normal equations for Ordinary Least Squares estimates we have B (m x 1 column vector) and X (n x m matrix). Could someone please convince me that the derivative with respect to B of B'X'XB is 2X'XB Thanks ! LR

I like Probability and Random Processes, Third Edition, by Grimmett and Stirzacker, (Oxford University Press, 2001).

This wasn't obvious to me. From my book. We have, p(x)=\begin{cases} \frac{1}{2} & -2\leq x\leq-1\,\textrm{or}\;1\leq x\leq2,\\ 0 & \text{otherwise~}.\end{cases} So, the kth moment is given by M_{k}=\frac{1}{2}\int_{-2}^{-1}x^{k}dx+\frac{1}{2}\int_{1}^{2}x^{k}dx So, obviously...

Thanks !

Can someone explain this.. P(v)=\frac{\beta}{\eta}\intop_{0}^{v}\left(\frac{v}{\eta}\right)^{\beta-1}\exp\left(-\left(\frac{v}{\eta}\right)^{\beta}\right)dv=\intop_{0}^{x}e^{-x}dx\hphantom{}\; where\phantom{\:}x=\left(\frac{v}{\eta}\right)^{\beta} Thanks !

Got it. Thanks again.