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A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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
Transcribed Image Text:### One-Generation Transition Probabilities Study
#### Overview
A study displays the one-generation transition probabilities among four major income groups. This data compares the income group of fathers and their eldest sons.
#### Transition Probabilities Table
The table below illustrates the probabilities of an eldest son transitioning between different income groups relative to their father's income group.
| Father's Income | Bottom 10% | 10%-50% | 50%-90% | Top 10% |
| --------------- | ----------- | ------------ | ---------- | --------- |
| **Bottom 10%** | 0.46 | 0.35 | 0.17 | 0.02 |
| **10%-50%** | 0.1 | 0.45 | 0.4 | 0.05 |
| **50%-90%** | 0.05 | 0.3 | 0.5 | 0.15 |
| **Top 10%** | 0.01 | 0.18 | 0.29 | 0.52 |
#### Analysis
The table above outlines the following key points:
- Eldest sons of fathers in the bottom 10% income group have a 46% chance to remain in the same income group.
- Sons of fathers in the top 10% income group have a 52% chance to remain in the top 10%.
- Mobility is especially noted within the 10%-50% and 50%-90% income groups, where sons have higher probabilities to stay within or move between these middle-income ranges compared to the extremes (bottom and top 10%).
#### Discussion Question
Given the transition probabilities outlined in the table, calculate the expected percentage of male earners in each category in the long term. (Round your answers to two decimal places.)
- **Bottom 10%**: ___________ %
- **10%-50%**: ___________ %
- **50%-90%**: ___________ %
- **Top 10%**: ___________ %
Need Help?
- Read more about economic mobility theory.
- Discuss your answers with a tutor.
*Note: Understanding these probabilities is essential for grasping the concept of economic mobility and how income groups can influence one's economic status over generations.*
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