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Suppose that a die is rolled twice. What are the possible
Chapter 4, Problem 7P(choose chapter or problem)
Problem 7P
Suppose that a die is rolled twice. What are the possible values that the following random variables can take on:
(a) the maximum value to appear in the two rolls;
(b) the minimum value to appear in the two rolls;
(c) the sum of the two rolls;
(d) the value of the first roll minus the value of the second roll?
Questions & Answers
QUESTION:
Problem 7P
Suppose that a die is rolled twice. What are the possible values that the following random variables can take on:
(a) the maximum value to appear in the two rolls;
(b) the minimum value to appear in the two rolls;
(c) the sum of the two rolls;
(d) the value of the first roll minus the value of the second roll?
ANSWER:
Solution:
Step 1 of 4:
If a die is rolled twice.
- The claim is to find the number of possible values that takes on the value to appear in the two rolls.
The possible values are 1, 2, 3, 4, 5, 6.
The total cases are = 36.
That is
(1, 1 ) |
(1, 2) |
(1, 3) |
(1, 4) |
(1, 5) |
(1, 6) |
(2, 1) |
(2, 2) |
(2, 3) |
(2, 4) |
(2, 5) |
(2, 6) |
(3, 1) |
(3, 2) |
(3, 3) |
(3, 4) |
(3, 5) |
(3, 6) |
(4, 1) |
(4, 2) |
(4, 3) |
(4, 4) |
(4, 5) |
(4, 6) |
(5, 1) |
(5, 2) |
(5, 3) |
(5, 4) |
(5, 5) |
(5, 6) |
(6, 1) |
(6, 2) |
(6, 3) |
(6, 4) |
(6, 5) |
(6, 6) |
For all (a, b), if ab the maximum is a, otherwise maximum is b.