# Math Help - Joint Densities

1. ## Joint Densities

A hand of six cards is dealt from a standard poker deck. Let X denote the number of aces, Y the number of kings, and Z the number of queens.
(a) Write a formula for pX,Y,Z(x,y,z).
(b) Find pX,Y(x,y)and pX,Z(x,z).

2. Originally Posted by donald17
A hand of six cards is dealt from a standard poker deck. Let X denote the number of aces, Y the number of kings, and Z the number of queens.
(a) Write a formula for pX,Y,Z(x,y,z).
(b) Find pX,Y(x,y)and pX,Z(x,z).
Won't (a) just be $\frac{{4 \choose x} \cdot {4 \choose y} \cdot {4 \choose z} \cdot {40 \choose (6 - x - y - z)}}{{52 \choose 6}}$ where $x + y + z \leq 6$.

Review multivariate hypergeometric distribution.