A researcher finds that two continuous, random variables of interest, X and Y, have a joint

Question

probability density function (pdf) given by:
f(x,y)={cxy 0<=x<=1,0<=y<=1,x+y=>1,
.........0 otherwise
where c is a constant.
(i) Find the value of c so that f(x,y) represents a pdf.
(iii) Calculate the conditional probability P{X > 0.25 | Y = 0.5}.
(iv) Calculate Cov(X,Y) and interpret the obtained value.
(v) Find E[X + 1/Y].

(ii) Calculate the marginal density functions of the random variables X and Y, and
E(X) and E(Y).