The following table gives the joint PDF of random variables X and Y, where X = the first-year rate of return (%) expected from investment A, and Y= the first-year rate of return (%) expected from investment B.

Rates of Return on Two investments
X(%)
Y(%) -10 0 20 30
20 0.27 0.08 0.16 0.00
50 0.00 0.04 0.10 0.35

a. Find the marginal distributions of Y and X.

b. Calculate the expected rate of return from investment B

c. Find the conditional distribution of Y, given X= 20

D. Are X and Y independent random variables? How do you know?