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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 fee of $100 plus $30 per defect. Let Y = the cost to repair the defects of the paint job of a car. What is the moment gener function of Y? For the instructor, this was question 8. X ek(e^t-1) X e(100+30k)(e^t-1) V e100t +k(e^30t-1) X e 100k +k(e^30t-1)

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 fee of $100 plus $30 per defect. Let Y = the cost to repair the defects of the paint job of a car. What is the moment gener function of Y? For the instructor, this was question 8. X ek(e^t-1) X e(100+30k)(e^t-1) V e100t +k(e^30t-1) X e 100k +k(e^30t-1)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**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. ❌ \( e^{100k+k(e^{30t}-1)} \)
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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