The joint density function of the random variables X and Y is given to the right.
(a) Show that X and Y are not independent.
(b) Find P(X > 0.3 | Y = 0.4).
f(x,y) = { 6x, 0 < x < 1, 0 < y < 1 - x
0, elsewhere
(a) Select the correct choice below and fill in the answer box to complete your choice.
A. Since f(x|y) = f(x,y) / h(y) = , for 0 < x < 1 - y, is constant, X and Y are not independent.
B. Since f(x|y) = f(x,y) / h(y) = , for 0 < x < 1 - y, is a function of only the variable x, X and Y are not independent.
C. Since f(x|y) = f(x,y) / h(y) = 3/4, for 0 < x < 1 - y, involves the variable y, X and Y are not independent.
D. Since f(x|y) = f(x,y) / h(y) = , for 0 < y < 1 - x, involves the variable x, X and Y are not independent.