How close are the experimental probabilities to the theoretical probabilities? Write a brief comparison of the theoretical and experimental probabilities. For which X values are the probabilities very close? Where is the biggest difference? How could you change the experiment to improve these estimates?
How close are the experimental probabilities to the theoretical probabilities? Write a brief comparison of the theoretical and experimental probabilities. For which X values are the probabilities very close? Where is the biggest difference? How could you change the experiment to improve these estimates?
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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Transcribed Image Text:# Tally and Probability Data Analysis
## Tally Data
The first table presents tally data with counts and percentages across different categories labeled under "C3." Here's a detailed breakdown:
- **C3 = 0:** Count is 1, representing 0.50% of the total.
- **C3 = 1:** Count is 2, representing 1.00% of the total.
- **C3 = 2:** Count is 7, representing 3.50% of the total.
- **C3 = 3:** Count is 27, representing 13.50% of the total.
- **C3 = 4:** Count is 53, representing 26.50% of the total.
- **C3 = 5:** Count is 51, representing 25.50% of the total.
- **C3 = 6:** Count is 36, representing 18.00% of the total.
- **C3 = 7:** Count is 21, representing 10.50% of the total.
- **C3 = 8:** Count is 2, representing 1.00% of the total.
**Total observations (N) = 200**
## Probability Analysis
The second table compares theoretical and experimental probabilities and calculates their differences for values of **X** ranging from 0 to 10.
### Table Columns:
- **X:** Discrete values for which probabilities are considered.
- **Theoretical Probability:** Calculated expected probabilities for each value of X.
- **Experimental Probability:** Actual observed probabilities, with some values not provided.
- **Difference:** The numerical difference between theoretical and experimental probabilities.
### Detailed Explanation:
- **X = 0:**
- Theoretical Probability: 0.0009
- Experimental Probability: Not provided
- Difference: Not provided
- **X = 1:**
- Theoretical Probability: 0.009
- Experimental Probability: 0.010
- Difference: 0.001
- **X = 2:**
- Theoretical Probability: 0.044
- Experimental Probability: 0.055
- Difference: 0.011
- **X = 3:**
- Theoretical Probability: 0.117
- Experimental Probability: 0.110
- Difference: -0.007
- **
Transcribed Image Text:**Comparison of Experimental and Theoretical Probabilities**
1. **Closeness to Theoretical Probabilities**: How close are the experimental probabilities to the theoretical probabilities?
2. **Comparison**: Write a brief comparison of the theoretical and experimental probabilities.
3. **Close Probabilities**: For which X values are the probabilities very close?
4. **Biggest Difference**: Where is the biggest difference?
5. **Improvement Suggestions**: How could you change the experiment to improve these estimates?
**Explanation**:
- This text prompts an exploration of the relationship between experimental and theoretical probabilities.
- Consider conducting a statistical analysis, noting where outcomes align or vary.
- Suggest modifications or methods to refine the experiment, possibly increasing repetitions or controlling variables, to enhance accuracy and reliability in probability estimates.
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