STAB52H3 Lecture Notes - Lecture 6: And1, Sequence, Borel Set
Document Summary
We have now studied, rather extensively, the probabilistic behaviour of a single random variable. The next issue we will address is the probabilistic relationship between two random variables x and y . One way of characterizing this relationship is by looking at their joint distribution. De nition 2. 7. 1 if x and y are random variables then the joint distribution of x and y is the collection of probabilities p ((x, y ) b), for all subsets b r2. Notice that in order for p((x, y ) b) to be well-de ned, x and y must be de ned on the same probability model. Remember, random variables are functions acting on the sample space and p is de ned on f. thus, it is incumbent that {(x, y ) b} = {s s : (x(s), y (s) b} belong in f.
