Don't Panic, Stochastic Calculus Edition

The midterm results are in, and they're not pretty. With a mean of 33 and a standard deviation of 18, we can safely say that this is not a normal distribution (assuming non-negative scores). It's been a while since I've taken an exam with such a low mean; it almost brings back nostalgia for the Engineering Math sequence. As I waited for the TA to find my test, a slew of 7s, 15s and 18s flashed by, and I began to silently hyperventilate. You know things are not good when your score < your age. Moreover, the stakes are higher now than in undergrad. I not only have my transcript, but $2,500 on the line, since the Fed won't reimburse me for tuition unless I get a C or above.

I knew this wasn't going to be an easy test, but I severely underestimated Prof Mykland's exam-writing abilities. Perhaps I should have known better when he related this anecdote on his PhD class: "I offered my class of ten students automatic As if they showed up for the exam...and 2-3 of them decided they'd rather skip it." When he announced that he wasn't allowing calculators, I thought that simply meant computations would be more tedious. In reality, that meant the exam would be completely theoretical.

In retrospect, perhaps I should have paced myself a bit better. We had 3 hours to complete 3 questions...and it wasn't nearly enough time for me. I ended up getting full credit for the first question, but by the time the 3rd question rolled around, I was so frustrated that I didn't even bother attempting to get partial credit, I just threw out the last page.

Anyways, I managed to beat the mean, though not by a healthy amount. Mykland reassured us that the vast majority of students receive As and Bs overall, and that if we did better on the final, those results would count in full. Never mind that the material covered on the final will be much harder. Mykland did say that he'd try to tone it down a bit for the final, since usually he gets means of "at least 40-50."

Student: "I understand that you don't want to write an exam that's too easy, but how am I supposed to feel about getting a 33 when I'm interviewing for jobs? If someone were to ask me about martingales, I would not say with confidence that I understand them very well."

Mykland: "Well, as evidenced by what's happening on Wall Street, I'd say a great many people don't understand them very well...if anything, I don't want to give anyone the illusion of understanding. The more you know, the more you realize you don't know."

Sigh. Okay, I can figure out the Itô integral of a deterministic integrand in the next three weeks...