The proportion of salt (X) and pepper (Y) left in the salt and pepper shakers at the end of a day at a crowded restaurant has a joint probability density function given by
f(x,y) = 3y for 0
a) Are X and Y independent?
b) What is the conditional density of X given Y=y?
c) What is the expectation of X given that Y = 0.5?
d) What is the expectation of X?