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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

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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**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 | |-----------|
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