Consider two continuous random variables X and Y with joint
p.d.f.
f(xy)=2 x^6 y 0x1 0y3x 0 otherwise
From HW 7, we have
fX(x)=9x^8 0x1 0 otherwise
fY(y)=2/7y1−(y/3^7) 0y3 0 otherwise
a. Are X and Y independent?
Find Cov(X, Y). Give your answer to 4 decimal places.
b. Find P(Y > 1 | X = 2/3). Give your
answer to 2 decimal place