Roll a pair of four-sided dice, one red and one black. Let \(X\) equal the outcome on the red die and let \(Y\) equal the sum of the two dice.

(a) On graph paper, describe the space of \(X\) and Y.

(b) Define the joint pmf on the space (similar to Figure 4.1-1).

(c) Give the marginal pmf of \(X\) in the margin.

(d) Give the marginal pmf of \(Y\) in the margin.

(e) Are \(X\) and \(Y\) dependent or independent? Why or why not?

Equation Transcription:

Text Transcription:

X

Y

Answer:

Step 1 of 6:

Given that, Roll a pair of four - sided dice, one red and one black, each of which has possible outcomes 1,2,3,4 that have equal probabilities.