joint probability distributions

#1
Hi, I am very puzzled as to how they achieved μ=2/5 in the example below. I understand that μ is just expected value which would mean summing x or y with its possible realizations. I'm thinking this is very obvious, however, I just can't see how they arrived at 2/5, which just proves I conceptually don't understand it. Any hints/help?
 

Attachments

staassis

Active Member
#2
Since the joint distribution is symmetric in X and Y the marginal distributions of X and Y are the same. You are given X's marginal density f_x(x). So

mu_y = mu_x = Int x * f_x(x) dx