The joint pdf of a two-dimensional RV (X, Y) is given by
f(x, y) = e^(-x-y), for x > 0, y > 0
= 0, elsewhere
a) Determine whether f(x, y) can serve as a joint pdf or not.
b) Find P(X < V).
c) Find P(Y < 1/2).
d) Find P(X > L, Y < 1/2).
e) Find the marginal pdf of X and Y.
f) Find the marginal CDF of X and Y.
g) Find P(K < Y).
h) Find P(X - Y < s).
i) Are X and Y independent? Find the conditional pdf f(x|y) and f(y|x).
k) Find P(X > I, Y < 1/2).
l) Find P(Y < 12 and X > 1).
m) Find Cov(2X + 5, 3Y).
n) Is X and Y uncorrelated? Find P(Y > 2X < 1).