Defining uncertainty
PROFESSOR: Uncertainty. When you talk about random variables, random variable Q, we've said that it has values Q1 up to, say, Qn, and probabilities P1 up to Pn, we speak of a standard deviation, delta Q, as the uncertainty, the standard deviation. And how is that standard deviation defined? Well you begin by making sure you know what is the expectation value of the-- or the average value of this random variable, which was defined, last time, I think I put braces, but bar is kind of nice sometimes too, at least for random variables, and it's the sum of the Pi times the Qi. The uncertainty is also some expectation value. And expectation value of deviation. So the uncertainty squared is the expectation value, sum over i, of deviations of the random variable from the mean. So you calculate the expected value of the difference of your random variable and the mean squared, and that is the square of the standard deviation. Now this is the definition. And it's a very ...