1) The joint pdf of (X, Y) is given below:
p(x,y) X
Y 0 1 2 3 p_Y(y)
1 0.05 0.10 0.30 0
0 0.02 0.05 0.15 0.05
-1 0.01 0.01 0.20 0.06
p_X(x)
a. Complete the table with the marginal pmf of X and Y
b. Fill in the table with joint cdf and marginal cdf's of X and Y:
F(x,y) X
Y 0 1 2 3 F_Y(y)
1
0
-1
F_X(x)
c. Use the joint CDF table to find P(0 < X ≤ 2, -1 < Y ≤ 1).