Tex, Slim and Billy are cowboys who have spent the week herding cattle. On Friday they go into town and get drunk. As they stagger out, each cowboys picks up a hat. Tex goes out first and randomly selects one of the three hats on the shelf. He is equally likely to select each of the three hats. Slim leaves second and he too randomly select each of the remaining two on the shelf. He is equally likely to select any. Billy leaves last and takes the one remaining hat. Let x be the number of cowboys who end up with the correct hat.

a) what is the prob distribution of X?
b) expected value
c) standard deviation