
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Transcribed Image Text:**Problem Statement:**
Let \( X \) be the number of defects on the paint job of a car which follows a Poisson distribution. To repair the defects costs a flat fee of $100 plus $30 per defect. Let \( Y \) be the cost to repair the defects of the paint job of a car. What is the moment generating function of \( Y \)?
*For the instructor, this was question 8.*
**Answer Choices:**
1. ❌ \( e^{k(e^t-1)} \)
2. ❌ \( e^{(100+30k)(e^t-1)} \)
3. ✅ \( e^{100t+k(e^{30t}-1)} \)
4. ❌ \( e^{100k+k(e^{30t}-1)} \)
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