Covariance

• August 1st 2011, 11:51 AM
thomasboateng
Covariance
The discrete variables A and B can each take any of the integer values {0,1,2,3}, and their joint
probability function is tabulated below.

B 0 1 2 3
A 0 |0.00 0.10 0.12 0.03
1 |0.15 0.20 0.08 0.02
2 |0.14 0.09 0.04 0.00
3 |0.02 0.01 0.00 0.00

a)Find the covariance of A and B.
b)Are A and B independent ? If not, then why not ?

i know for covariance the forumula is cov= E[AB]-E[A]E[B]
I have E[A]=1.08 ,E[B]=1.03, Var[A]=0.6336, Var[B]=0.7491

so yeah i kinda need help with the E[AB] part
• August 4th 2011, 09:30 AM
Moo
Re: Covariance
Hello,

You'll have to compute the probabilities for the values of AB.

AB can only equal 0,1,2,3,4,6.

0 : A or B is 0, that is .15+.14+.02 + .10+.12+.03
1 : A=1, B=1 that is .20
2 : A=1, B=2 or A=2,B=1 that is .09+.08

etc...
• August 4th 2011, 07:53 PM
mahefo
Re: Covariance
You can use formula
$\mathbb E(AB) =\sum_{\text{all cases } a,b} a b \mathbb P (A=a, B=b)$