Black Swans


1 points

cunic hasn't added a bio yet


This means some tiny change in x. So you're effectively computing the probability at an exact point since δx goes to 0. It's really just saying that p(x) is a function that computes the probabilities of variable x being any of its possible values.

The interval (a,b) part means you can compute the probability of x landing in an range from a to b by taking the integral of p(x).

Another way to phrase the whole paragraph is: If p(x) tells you the probability of x landing at a particular value, to compute the likelihood x lands in interval (a,b) just take the integral of the probability density function over that range.