“The journey not the arrival matters.” - T. S. Eliot
It is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth.
–Benjamin Peirce, a noted nineteenth century mathematician and Harvard professor, after proving the Euler Identity (e^{i \pi}=-1)
I'll have to figure out a way for this site to display LaTeX output, it'd work much better…
Delta Method: Let \hat{\phi} be an estimate of \phi based on a sample of size n such that \sqrt{n}{\hat{\phi}-\phi} is asymptotically normal with mean 0 and variance \sigma^2. Then for any function h, where h is differentiable and h'(\phi) \ne 0, we have \sqrt{n}{h(\hat{\phi})-h(\phi)} is distributed as N(0, \sigma^2 |h'(\phi)|^2). In other words, h(\hat{\phi}) is approximately normally distribued with mean h(\phi) and variance var(\hat{\phi})|h'(\phi)|^2.
Magic Formula: p*_\theta(\theta) = c(\theta) (2\pi)^{-1/2} |I(\hat{\theta})|^{1/2} \frac{L(\theta)}{L(\hat{\theta})}, where c(\theta) is a generic normalizing constant
Wald Test: z = \frac{\hat{\theta}-\theta}{I(\hat{\theta})} ~ N(0,1)
Score Test: z = \frac{S(\theta)}{\sqrt{\mathcal{I}(\theta)}} ~ N(0,1)
Likelihood Ratio Test: W = -2 \ln \frac{L(\theta)}{L(\hat{\theta})} ~ \chi^2_1
Cochran's Theorem: If Y ~ N(0,\sigma^2 I_n) and A_i are idempotent matrices with rank(A_i)=r_i and \sum_{i=1}^{m} A_i = A, then \frac{1}{\sigma^2}y'A_i y are independently distributed as X^2_{r_i} if and only if \sum_{i=1}^{m} r_i = n.
For the theory qual that is (June 9th)… it's a long list, and kinda scary:
There was a piece on slate.com this week about what needs to change in the liberal arts education. Here’s an excerpt:
I start with two problems. One is most evident with humanities majors: Many of them don’t know how to evaluate mathematical models or statistical arguments. And I think that makes you incompetent to participate in many discussions of public policy. So I favor making sure that someone teaches a bunch of really exciting courses, aimed at non-majors in the natural and social sciences, which display how mathematical modeling and statistical techniques can be used and abused in science and in discussions of public policy. If there are enough of them and they’re good enough, one or two required courses in this area won’t seem like a chore to students. And even those who grouse will probably be grateful later. Learn Bayes’ Theorem, it won’t kill you.
The second problem is one that you can find in almost every major, though it’s less common among those doing foreign-language majors or area studies. It is an astonishing parochialism. (This is, for obvious reasons, less common among students from abroad.) Too many of our students haven’t the faintest idea what life is like anywhere outside the class and the community—let alone the country—they grew up in. Language requirements—that you should leave college with one more language than you entered with, say—can help here. And so, no doubt, can courses on other places, peoples, and times.
Also, Ehty forwarded this hilarious HP4 film review from a very reliable source. 
The Japanese eat very little fat and suffer fewer heart attacks than the British or the Americans.
On the other hand, the French eat a lot of fat and also suffer fewer heart attacks than the British or the Americans. The Japanese drink very little red wine and suffer fewer heart attacks than the British or the Americans. The Italians drink excessive amounts of red wine and also suffer fewer heart attacks than the British or the Americans.
Conclusion: Eat and drink whatever you like. It’s speaking English that kills you.