Joint Distribution of U=aX+b, V=cY+d

So my wife and I have talked quite a bit about my "interview" on Tuesday. It's just an interview for an internship, but internships are very important.

If I were chosen, I'd have a tough decision to make -- first, if I am also accepted for the Ph. D. program, do I abandon that? Face it, as a Ph. D. student, I'd be working for four years at a pittance with no guarantee of a Ph. D. Second, if I take the internship, and are offered a job, then if I have to work in California, do we move there?

A few things have already been decided. If I am offered the internship, I'll go to an Extended Stay Hotel to live. It's basically a room with a bed, a TV, a shower and a sink. I'll live there for 10-12 weeks. We figure that I'll break even, but the advantage is that I'll make connections in the industry. I'll probably use my wife's car while I'm there.

Right now, I have a quiz in Intro Statistics do tomorrow -- the quiz is about the binomial and normal distributions, which we've discussed ad nauseam in all of my probability classes. I'm not too worried about the quiz, although you never know.

On Monday, we have not only an exam in Intro Stats, but we also have a problem set to turn in to Math Foundations (run by Dr. S). Those are some of the hardest programs I've ever seen. I doubt that any of them would show up on Exam P. For example, there are a lot of problems of the type U=X+Y and V=X/Y where X and Y are random variables and you are to find g(U, V). The ACTEX manual explains the solution nicely -- it depends on a Jacobian, the difference of individual products of partial differentials -- but we've never been taught the method in any classes and certainly, not in this one.

Dr. S says "I don't expect you to get all of these problems." Once again, he leaves his expectations unnamed. I wonder if he's a fan of Robert Pirsig, who wrote "Zen and the Art of Motorcycle Maintainence" who did not believe in grading, because he wanted his students to become knowledge-motivated and not grade-motivated.

In actuarial science, this might be impossible. Everyone in that room is grade-obsessed, even me. I'd like to be knowledge-obsessed, but it can be hard. Haven't done as much as I'd like to this weekend. We'll see how tomorrow goes.