The joint probability function of two discrete random variables X and Y is given by P(xi, yj) = K(2xi + yj), where K is a constant. X and Y can assume the following integer values: xi = 0, 1, 2 and yj = 0, 1, 2, 3. P(x, y) = 0 otherwise.
Q1 (5pts):
a) Find the value of the constant K so that this probability distribution is valid. Hint: Construct a table for the joint probability distribution to help you see the distribution.
Q2 (5pts):
b) Find P(X=2, Y=1).
Q3 (5pts):
c) Find P(X≥1, Y≤2).
Q4 (5pts):
d) Give the marginal distributions for X and for Y: P(X) and P(Y).
Q5 (5pts):
e) Show that X and Y are not independent.
Q6 (5pts):
f) Determine the value of the correlation coefficient of X and Y. Interpret your result.