ABSTRACT
From the table of probabilities, it is clear that ≤ ≤p x y0 ( , ) 1
∑∑ = + + + + + + + + + + + + + + + + + =
p x y( , ) 0 0.050 0.025 0 0.025 0 0.200 0.050 0 0.300
0 0 0.100 0 0 0 0.100 0.150 1 xy
b. To find the marginal probability distribution for X, we need to find =P X( 0) , =P X( 1) , =P X( 2) , =P X( 3) , =P X( 4) , =P X( 5) . Since =X 0 can occur when
=Y 0,1 or 2 occurs, then = =P X p( 0) (0)1 is calculated by summing the probabilities of 3 mutually exclusive events:
= = = + + = + + =P X p p p p( 0) (0) (0,0) (0,1) (0, 2) 0 0.200 0.100 0.3001 Similarly, = = = + + = + + =P X p p p p( 1) (1) (1,0) (1,1) (1, 2) 0.050 0.050 0 0.1001 = = = + + = + + =P X p p p p( 2) (2) (2,0) (2,1) (2, 2) 0.025 0 0 0.0251 = = = + + = + + =P X p p p p( 3) (3) (3,0) (3,1) (3, 2) 0 0.300 0 0.3001 = = = + + = + + =P X p p p p( 4) (4) (4,0) (4,1) (4, 2) 0.025 0 0.100 0.1251 = = = + + = + + =P X p p p p( 5) (5) (5,0) (5,1) (5, 2) 0 0 0.150 0.1501 The marginal distribution p x( )1 is given as:
c. The marginal probability distribution for Y is found as in part a.
