Let X Y be two Bernoulli random variables with the joint pmf

Let X, Y be two (Bernoulli) random variables with the joint p.m.f. p(0; 0) = 0:3, p(0; 1) = p(1; 0) = 0:2, and p(1; 1) = 0:3.

What are the marginal p.m.f.\'s of X and Y ?

Are X and Y independent?

Calculate cov(X; Y ) and corr(X; Y ).

Solution

pmf for X

x  

0    0.2 + 0.3 = 0.5

1   0.3 + 0.2 = 0.5

pmf for Y

0    0.3 + 0.2 = 0.5

1    0.2+0.3 = 0.5

yes they are independent

for the other question

you should post it in a new question