You have two fair dice, one with three sides labeled 0,1,2 and one with 4 sides, labeled 0, 1, 2, 3. Let X1 be the outcome of rolling the first die, and X2 the outcome of rolling the second. The rolls are independent. a. What is the joint distribution of (X₁, X₂)? b. Let Y₁ = X₁ X₂ and Y₂ = max{X₁, X₂}. Make a table for the joint distribution ofY₁, Y₂. c. What are the marginal distribution of Y₁, Y₂? Are they independent?