"Probabilities can be used in two ways. 1. Probabilities can describe frequencies of outcomes in random experiments 2. Probabilities can also be used, more generally, to describe degrees of belief in propositions that do not involve random variables This more general use of probability to quantify be"
"The details of the other possible outcomes and their probabilities are irrelevant. All that matters is the probability of the outcome that actually happened (here, that the ball drawn was black) given the dierent hypotheses. We need only to know the likelihood, i.e., how the probability of the data "
"Entropy is maximized if p is uniform: [;H(X) \leq log(|A_X|);] with equality iff [;p_i = 1/|A_X|;] for all i."
"a disk drive is an example of communication, which doesn't have to involve information going from one place to another. When we write a file on a disk drive, we'll read it off in the same location - but at a later time."