Solution Found!
Roll a pair of four-sided dice, one red and one black. Let X equal the outcome on the
Chapter 4, Problem 4.1-3(choose chapter or problem)
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?
Questions & Answers
QUESTION:
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?
ANSWER:Problem 4.1.3
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?
Step by Step Solution
Step 1 of 4
a) Both dies are 4 sided hence the probability space for X is
The space Y is the sum of outcomes on the two die so the space Y is given by
The space for X and Y is depicted in the figure below:
