let x1 and x2 have the joint pmf px1x2 described as follows

let x1 and x2 have the joint pmf p(x1,x2) described as follows and p(x1,x2) is equal to zero elsewhere. Find the two marginal probability mass functions and the two conditional means. Hint: write the probabilities in a rectangular array.

(x1,x2): (0,0), (0,1), (1,0) (1,1) (2,0) (2,1)

p(x1,x2): 1/18 3/18 4/18 3/18 6/18 1/18

Solution

PMF table is given by:

Marginal distribution of x1:

P(x1=0) = 1/18 + 3/18 = 4/18

P(x1=1) = 4/18 + 3/18 = 7/18

P(x1=2) = 6/18 + 1/18 = 7/18

Mean of x1: 0*4/18 + 1*7/18 + 2*7/18 = 21/18

Marginal distribution of x2:

P(x2=0) = 1/18 + 4/18 + 6/81 = 11/18

P(x2=1) = 3/18 + 3/18 + 1/18= 7/18

Mean of x2: 0*11/18 + 1*7/18 = 7/18