Question

Let X₁ and X₂ have the joint pmf p(x₁,x₂)=x₁x₂/36 ,x₁=1,2,3 and x₂=1,2,3, zero elsewhere.

Obtain the joint pmf of Y₁=X₁X₂ and Y₂=X₂, and the marginal pmf of Y₁.

Answer 1

joint pmf of Y₁=X₁X₂ and Y₂=X₂:

$p(1,1)=1/36, p(2,2)=2/36, p(3,3)=3/36, p(2,1)=2/36, p(4,2)=4/36,$

$p(6,3)=6/36, p(3,1)=3/36, p(6,2)=6/36, p(9,3)=9/36$

marginal pmf of Y₁:

$p(1)=1/36$

$p(2)=2/36+2/36=4/36$

$p(3)=3/36+3/36=6/36$

$p(4)=4/36$

$p(6)=6/36+6/36=12/36$

$p(9)=9/36$