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Roll a pair of four-sided dice, one red and one black, each of which has possible
Chapter 4, Problem 4..1-2(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?
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?
ANSWER:Problem 4.1.2
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?
Step by Step Solution
Step 1 of 5
A pair of four – sided dice are rolled, 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.
Then,
The set of all possible outcomes i.e. the sample space S of X and Y is
