Going over past papers, and i cant seem to interpret this question properly, and dont know if my answer is correct;

Suppose random variables X and Y are independent and each had a bernoulli distribution with parameter p = 0.5. Define Z= | X - Y |

(i) Write down all the possible values of (X,Y) and the corresponding values of Z. Hence verify that Z also has a bernoulli distribution with parameter p = 0.5

Im unsure of what its asking for.

I know that X(success) = 1, X(failure) = 0, Y(success) = 1, Y(failure) = 0

Therefore this would mean values of Z = 0,1 with the probability of each being 1/2, therefore this means parameter p for z = 0.5

Is this correct so far?