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f(x,y) = 2 if 0 <= y <= x <= 1

and 0 otherwise

a) calculate the marginal probability density functions.

f(x) = 2x

f(y) = 2-2y

b) find E(X) and E(Y).

E(X) = 2/3

E(Y) = 1/3

c) calculate P(X<1/2) , P(X<2Y) and P(X=Y).

P(X<1/2) = integral from 0 to 1/2 of 2x dx = 1/4

but as for the other 2 I have no idea on how to do them. do they also involve the marginal distribution functions? Any help as always is greatly appreciated.

Thanks.