---
title: "Assignment 3: Responses"
author: "Your name"
format:
  pdf:
    documentclass: scrartcl
    fontsize: 11pt
    geometry: margin=1in
---

**STAT 8670 | Fall 2026**  
**Due date:** Monday, November 2, 2026  
**Total:** 30 points  
**Coverage:** Main Chapter 4 material; Supplementary and optional topics are excluded.

Submit your completed source and rendered PDF as `A3_LastName_FirstName.qmd` and `A3_LastName_FirstName.pdf`. See the assignment for the full questions. Each item is worth 1 point.

R code and plots are optional. If you generate random values, set a seed (e.g., `set.seed(8670)`) and include the code in your source file.

## Questions 1-3: Answer Table

Enter **one letter** for each multiple-choice item and **True** or **False** for each statement. No explanations are needed for Questions 1-3.

| Question 1 | Answer | Question 2 | Answer | Question 3 | Answer |
|:---:|:---:|:---:|:---:|:---:|:---:|
| 1a | | 2a | | 3a | |
| 1b | | 2b | | 3b | |
| 1c | | 2c | | 3c | |
| 1d | | 2d | | 3d | |
| 1e | | 2e | | 3e | |
| 1f | | 2f | | 3f | |
| 1g | | 2g | |  | |
| 1h | | 2h | |  | |

## Question 4a: A Normal Mixture [4]

- **4a.1 Correct mixture generator:** [Your response.]
- **4a.2 Two means and whether they reveal the error:** [Your response.]
- **4a.3 Variance of the target mixture and of $W$:** [Your response.]
- **4a.4 Comparing distributions after rescaling; one additional check:** [Your response.]

## Question 4b: Checking an Exponential Generator [4]

- **4b.1 Theoretical mean and variance:** [Your response.]
- **4b.2 Parameter error and corrected R call:** [Your response.]
- **4b.3 Histogram and target-density check:** [Your response.]
- **4b.4 Whether more observations would fix the error, and why:** [Your response.]

<!-- If you use R to check an answer, include the code after your responses. -->