Here's the statement for **Problem 3** from your homework: ### **Problem 3 (9=3+3+3 points)**: Measurements are made of the length \( L \) and width \( W \) of a rectangular part. Assume that: - \( L \sim U(9.95, 10.05) \) (i.e., \( L \) follows a **uniform distribution** on the interval [9.95, 10.05]), - \( W \sim U(4.9, 5.1) \) (i.e., \( W \) follows a **uniform distribution** on the interval [4.9, 5.1]). Also, assume that **\( L \)** and **\( W \)** are **independent random variables**. For each of the following events: 1. **(a)** Express them using **set notation**, 2. **(b)** Draw them in the **joint sample space** of \( (L, W) \), 3. **(c)** Calculate their **probability**. --- ### Questions: 1. The length is less than 9.98. 2. The length is between 9.96 and 9.98 and the width is between 5.0 and 5.05. 3. Either the length is between 9.96 and 9.98, or the width is between 5.0 and 5.05. --- Let me know if you'd like to begin working on any part of Problem 3! I'll guide you through the concepts, and we can use examples to help you solve it