1. ## joint pmf covariance

I have a joint p.m.f. but am very stuck with how to find the following:
1) covariance
2) correlation coefficient of X and Y
3) If X and Y are independent

I already calculated the marginal p.m.f.s, means and variances from my data which is as follows:

x__ 1___ 2___ 3___ 4___ 5
y
3__.02_ .03_ .06__ .15_ .07
2__.02_ .05_ .08__ .12_ .06
1__.05_ .05_ .06__ .13_ .05

2. Originally Posted by antman
I have a joint p.m.f. but am very stuck with how to find the following:
1) covariance
2) correlation coefficient of X and Y
3) If X and Y are independent

I already calculated the marginal p.m.f.s, means and variances from my data which is as follows:

x__ 1___ 2___ 3___ 4___ 5
y
3__.02_ .03_ .06__ .15_ .07
2__.02_ .05_ .08__ .12_ .06
1__.05_ .05_ .06__ .13_ .05
1) If you know to compute mean of a random variable, covariance is not too hard. Covariance(X,Y) = E(XY) - E(X)E(Y). Thus first compute the mean of the product random variable XY

2) $\text{Correlation} = \frac{Cov(X,Y)}{\sqrt{\text{Var}(X)\text{Var}(Y)}}$

3) If Covariance is non -zero, the random variables are definitely not independent

3. I know how to find E(X) and E(Y), the means 3.45 and 1.99 respectively, but how do I find E(XY)? Thank you for your help!

4. I think I figured it out. I got covariance=7.01-3.45(1.99)=0.1445? Therefore, x and y are not independent. Is this correct?
Also, how do I find the least squares regression line?

Thank you!