Solution Found!
Roll a pair of four-sided dice, one red and one black,
Chapter 4, Problem 2E(choose chapter or problem)
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. Let \(X\) equal the outcome on the red die, and let \(Y\) equal the outcome on the black die.
(a) On graph paper, show 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
1,2,3,4
Questions & Answers
QUESTION:
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. Let \(X\) equal the outcome on the red die, and let \(Y\) equal the outcome on the black die.
(a) On graph paper, show 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
1,2,3,4
ANSWER:
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.