Yes, sort of. But I think he says a lot of unnecessary things not getting at the root of the issue.
I left out some detail I should have said, like what is so special about a gaussian that makes the math easy. So I will say it.
A measurement can infer a probability distribution for what the measured quantity is. A second measurement, on its own, also infers some probability distribution for what the measured quantity is. It we consider both measurements together, we get yet another probability distribution for what the measured quantity is. The magic is that if we had a gaussian distribution for the measurements, then the distribution for the combined measurements is also a gaussian. This is not true in general. As long as we have gaussian distributions we can do all the operations we want and the probability distributions are gaussian and can be fully described by a center point and a width. (Forgive me for the liberties I am taking here.) The basic alternative to exactly solving the problem is to actually try to carry around the probability distribution functions, which is not practical even with very powerful computers.
I left out some detail I should have said, like what is so special about a gaussian that makes the math easy. So I will say it.
A measurement can infer a probability distribution for what the measured quantity is. A second measurement, on its own, also infers some probability distribution for what the measured quantity is. It we consider both measurements together, we get yet another probability distribution for what the measured quantity is. The magic is that if we had a gaussian distribution for the measurements, then the distribution for the combined measurements is also a gaussian. This is not true in general. As long as we have gaussian distributions we can do all the operations we want and the probability distributions are gaussian and can be fully described by a center point and a width. (Forgive me for the liberties I am taking here.) The basic alternative to exactly solving the problem is to actually try to carry around the probability distribution functions, which is not practical even with very powerful computers.