How Do You Calculate Covariance from a Joint Probability Table?

[Gregg]

A bag contains three green beads, two red beads and a blue bead. You select
two beads at random. Let G denote the number of green beads and R the
number of red beads you select.

(a) Write the joint probability distribution of (G,R) in a table. Show that
Cov(G;R) < 0.


I can do P(G=g) for g=0,1,2 and P(R=r) for r=0,1,2. but isn't f(g,r) is not equal to P(G=g)P(R=r)? Is it?

 

[tiny-tim]

Hi Gregg!

Try the easy case:

is P(G = R = 0) = P(G = 0)P(R = 0) ?

 

[Gregg]

0,4/15,1/15
6/15,3/15,0
1/15,0,0

That's the table I got for G (0,1,2) in column and R(01,2) in row. Giving E(G)=11/15 and E(R)=9/15.

Is covariance just $\sum_g\sum_r (g-E[G])(r-E[R])P(G=g,R=r)$ ? Is there a quicker way to compute this?

calculate E(G | R = r).