Let x and y have the joint p.m.f. given by:

$\displaystyle

\begin{pmatrix}&&&x&&\\y&1&2&3&4&5\\3&0.02&0.03&0. 06&0.15&0.07\\2&0.02&0.05&0.08&0.12&0.06\\1&0.05&0 .05&0.06&0.13&0.05\end{pmatrix}

$

a) Find the marginal p.m.f.s and the means and variances.

b) Are x and y independent? Why?

c) Find the covariance and the correlation coefficient of x and y.

I appreciate any help. I don't know how a problem like this is done so can't do the rest of them. Thank you so much