Celebrate the Small Successes

Derive the variance of B, I read. No problem, I can derive a variance in my sleep. Hum, prove B is unbiased first. Done and done, now the variance. I started to put the variance through its paces. I put the expectation operator through the expression and then realised to my horror that nothing cancelled out. I had an expression that barely fit across the page and it would not simplify. I was on the verge of panicking. I had another fourteen marks riding on this answer as I needed it for the next part. Dumbfounded at my inability to identify the simplifying factor, I moved on, knowing that I would be back.

On the second time attacking the question, I stared at my cheat sheet trying to gain some insight. There was only one thing that I could try and I couldn't see how that would help. But then it hit me, if I did that, it would form a projection matrix - at least I would be able to fit the expression on one line. Attempting now to prove that one variance minus another was positive semi definite, I wrote out the equation and did the first step as always. There was no way this was getting the better of me. As my frustration level grew, I started to tap my pencil on the table, faster and louder - until I got the look. So I stopped and pounded the table mentally. Fourteen bloody marks and I was not going to give them up. I could fail the rest of the exam but this question I was going to master. I looked at my example and then something struck me. What if I treated this nasty part here, like this omega here on the sheet, it might just work. And work, it did, like a charm.

I was relieved, knowing that everyone else would have been able to answer that question and that for once I had not been the dunce. That is until lunch when it started to seem that not everyone had been able to do it. Then I was back in a game I could play. Instead of keeping quiet pretending that I had gotten something, I was just quiet - almost. Except that in my surprise that no one else had gotten it, I blurted out "I got it." but I stopped just short of explaining how. The expression wouldn't fit across my napkin.