Answer:
Yes. Have the same distribution.
Step-by-step explanation:
Given that X is a random day of the week, coded so that Monday is 1, Tuesday is 2, etc. (so X takes values 1, 2,..., 7, with equal probabilities).
Y is the next day after X
So Y can be written as X+1
But since highest value is 7, we can write
Y = X+1 mod 7
i.e. whenever X=7, Y= 8= 1 again.
Thus Y can take values as
Y 1 2 3 4 5 6 7
P(Y) = P(X+1) = 1/7
i.e. Y also has the same distribution as X
