## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

# Vector valued random variables

## 4.1   Joint distribution

Let X and Y be two random variables. The distribution vector does not bear enough information about the relations occurring between X and Y, for instance to compute where A and B are generated by X and Y, respectively; one needs to introduce a new object called the joint (probability) distribution of X and Y.

Example 4.1 (Discrete random variables) Let X and Y be two discrete random variables on the same probability space . Let , and let (p1, . . ., pn) and (q1, . . ., qm) be the mass density vectors of and , respectively.

The image of the map (X, Y) : Ω → is a subset of {(xi, yj), i = 1, . . ., n, j = 1, . . ., m} (whose cardinality ...

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required