The joint probability density function of the two continuous RVs X and Y is
FX,Y(x,y) = cxy 0
= 0 otherwise
a) Find out the value of the constant c
b) Find out P (1 < X < 2, 2 < Y < 3)
c) Find out the marginal probability distribution functions of X and Y
d) Find out the conditional probability distribution function of X given Y=2
e) Are X and Y independent?
f) Compute the expectation values of X, Y and 2X + 3Y
Please show all work and extra karma will be awarded for multiple parts (just post each section with work)