A spinner marked off in three equal-sized regions, numbered 1, 2, and 3, is spun twice. Let the random variable X be the nonnegative difference between the numbers of the regions where the pointer stops, and define a probability mass function g(x)=P(X-x) a) State the range of X b) Write g as a set of t of ordered pairs. c) Draw a probability distribution as a histogram. d) Find g(0), and explain what this number represents. e) Find and explain what this number represents. a) What is the range of X? OA. (1.2) OB. (0.1.2) OC. (1, 2, 3, 4) OD. (0. 1. 2. 3. 4) b) Write g as a set of ordered pairs. Choose the correct answer below. OA ( ) ( ) ( ) OB. Oc (-)-(¹)-(²) (¹)-(²)· (~ 3) OD e) Which of the following is the correct histogram of the probability distribution? OA Ос ▬ OB.
A spinner marked off in three equal-sized regions, numbered 1, 2, and 3, is spun twice. Let the random variable X be the nonnegative difference between the numbers of the regions where the pointer stops, and define a probability mass function g(x)=P(X-x) a) State the range of X b) Write g as a set of t of ordered pairs. c) Draw a probability distribution as a histogram. d) Find g(0), and explain what this number represents. e) Find and explain what this number represents. a) What is the range of X? OA. (1.2) OB. (0.1.2) OC. (1, 2, 3, 4) OD. (0. 1. 2. 3. 4) b) Write g as a set of ordered pairs. Choose the correct answer below. OA ( ) ( ) ( ) OB. Oc (-)-(¹)-(²) (¹)-(²)· (~ 3) OD e) Which of the following is the correct histogram of the probability distribution? OA Ос ▬ OB.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:### Probability Distribution and Expected Value of a Spinner
#### Problem Statement
A spinner marked off into three equal-sized regions, numbered 1, 2, and 3, is spun twice. Let the random variable X be the nonnegative difference between the numbers of the regions where the pointer stops, and define a probability mass function g(x) = P(X = x). Complete the following:
a) State the range of X.
b) Write X as a set of ordered pairs.
c) Draw a probability distribution as a histogram.
d) Find g(0), and explain what this number represents.
e) Find µ, and explain what this number represents.
#### Solution
a) **What is the range of X?**
- The range of X can be found by considering the possible nonnegative differences between the regions where the pointer stops.
- **Answer Options:**
- A. {1, 2}
- B. {0, 1, 2}
- C. {1, 2, 3}
- D. {0, 1, 2, 3}
- **Correct Answer:**
- B. {0, 1, 2}
b) **Write X as a set of ordered pairs. Choose the correct answer below:**
- To write X as a set of ordered pairs, consider each pair of spins and their difference.
- **Answer Options:**
- A. {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
- B. {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} with respective differences as needed
- C. {(x,y)} such that x-y is the nonnegative difference
- D. {(x,y)} such that the set represents unique nonnegative differences
- **Correct Answer:**
- B. \[\left\{ (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3
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