This is the question, from a practice final for a stat course:
The Intel Pentium Processor chip has been discovered to make small errors occasionally; that is, errors of +1 or –1 (in $10^{-4}$ units) in a small fraction of its calculations. Suppose that these occur in a single calculation with probability 0.0005 each, and that otherwise the results are correct. Suppose further that positive and negative errors are equally frequent. An Intel engineer discovers a partial “fix” that would eliminate the chance of negative errors by making all errors positive (so the chance of a positive error would become 0.001). Which chip would have smaller Mean Squared Error for a single calculation, old or new?
I'm having trouble starting (with a start, I think I could figure it out). I know that $MSE = E[(\theta+\hat\theta)^2]$, so I tried to say that for part I the expected error is $.0005(-.0001)+.0005(.0001)=0$ and for part II the expected error would be $.001(.0001)=.0000001$ so the second would have a higher MSE, but that doesn't seem intuitively correct. I may be messing up something obvious -- way to long in the library today.