Assume that we have a two-dimensional random vector Z = [X, Y] such that
X = 5cosθ
and Y = 5sinθ
where θ is a discrete uniform random variable in the set {0, 1, 2, 3, 4, 5, 6, 7}.
a) Identify the range Sxy of the pair (X, Y).
b) Find the joint PMF of X and Y.
c) Find the marginal PMF of X.
d) Find the marginal PMF of Y.
e) Find the probability of the following events:
A = {X = 0}
B = {Y > 5/2}
C = {X < 2}