Two components of a computer have the following joint pdf for their useful lifetime X and Y (in years):

f(x,y) = { 2/5 (2x + 3y), 0 x 1 and 0 y 1;

0, otherwise

Find

(i) the marginal pdf of Y (the useful lifetime of the 2nd component);

(ii) the conditional pdf of X given that Y= 1/3;

(iii) the expected value of X given that Y = 1/3.