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?