An incomplete contingency table is provided. Use this table to complete the following. a. Fill in the missing entries in the contingency table. b. Determine P(C, ), P(R2), and P(C, & R2). c. Construct the corresponding joint probability distribution. C, C2 Total O R, 16 R2 7 Total 40

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
100%
**Educational Website Content: Transcribing and Analyzing a Contingency Table**

In this exercise, an incomplete contingency table is provided, and you will use it to complete various tasks related to probabilities.

### Tasks:

a. **Complete the Contingency Table:**

Given values:

- \( R_1C_1 = 5 \)
- \( R_1 \) Total = 16
- \( R_2C_2 = 7 \)
- Total = 40

To complete the table, fill in the missing values:

|      | \( C_1 \) | \( C_2 \) | Total |
|------|-------|-------|-------|
| \( R_1 \) | 5     | 11    | 16    |
| \( R_2 \) | 19    | 7     | 26    |
| Total | 24    | 18    | 40    |

Find the missing values by solving the following:
- \( R_1C_2 = R_1 \text{ Total} - R_1C_1 = 16 - 5 = 11 \)
- \( R_2C_1 = \text{Total } C_1 - R_1C_1 = 24 - 5 = 19 \)
- \( \text{Total } C_2 = R_1C_2 + R_2C_2 = 11 + 7 = 18 \)

b. **Find Each Probability:**

1. \( P(C_1) = \frac{\text{Total for } C_1}{\text{Grand Total}} = \frac{24}{40} = 0.60 \)
2. \( P(R_2) = \frac{\text{Total for } R_2}{\text{Grand Total}} = \frac{26}{40} = 0.65 \)
3. \( P(C_1 \text{ & } R_2) = \frac{R_2C_1}{\text{Grand Total}} = \frac{19}{40} = 0.475 \)

c. **Complete the Joint Probability Distribution:**

To find the joint probability, divide each entry by the grand total (40):

|           | \( C_1 \)   | \( C_2 \)  | Total |
|-----------|
Transcribed Image Text:**Educational Website Content: Transcribing and Analyzing a Contingency Table** In this exercise, an incomplete contingency table is provided, and you will use it to complete various tasks related to probabilities. ### Tasks: a. **Complete the Contingency Table:** Given values: - \( R_1C_1 = 5 \) - \( R_1 \) Total = 16 - \( R_2C_2 = 7 \) - Total = 40 To complete the table, fill in the missing values: | | \( C_1 \) | \( C_2 \) | Total | |------|-------|-------|-------| | \( R_1 \) | 5 | 11 | 16 | | \( R_2 \) | 19 | 7 | 26 | | Total | 24 | 18 | 40 | Find the missing values by solving the following: - \( R_1C_2 = R_1 \text{ Total} - R_1C_1 = 16 - 5 = 11 \) - \( R_2C_1 = \text{Total } C_1 - R_1C_1 = 24 - 5 = 19 \) - \( \text{Total } C_2 = R_1C_2 + R_2C_2 = 11 + 7 = 18 \) b. **Find Each Probability:** 1. \( P(C_1) = \frac{\text{Total for } C_1}{\text{Grand Total}} = \frac{24}{40} = 0.60 \) 2. \( P(R_2) = \frac{\text{Total for } R_2}{\text{Grand Total}} = \frac{26}{40} = 0.65 \) 3. \( P(C_1 \text{ & } R_2) = \frac{R_2C_1}{\text{Grand Total}} = \frac{19}{40} = 0.475 \) c. **Complete the Joint Probability Distribution:** To find the joint probability, divide each entry by the grand total (40): | | \( C_1 \) | \( C_2 \) | Total | |-----------|
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman