---
# System prepended metadata

title: Exam 1
tags: ['teach:MS']

---

---
title: Exam 1
tags: teach:MS
---

# Exam 1


## 題目考點分析

|No| Chapter | 所需微積分|
| --|----|---|
| 1 | 2. Probability, conditional probability | No 
| 2a| 3. Probability of a Exponential distribution  | Integration| 
| 2b| 4.1 Markov inequality | Integration|
| 3a| 3. cdf of $Y/X$ | integration, or calculation of area 
| 3b| 3. density of $Y/X$ | differentiation|
| 4a| 2. $a+bX$ | integration and diff|
|4b| 2. $Z^2$| integration and differentiation|
|5| 4. Definition of expectation |  Beta function| 
|6a| 3.7. order statistics, Beta distributions  |  | plug in formula
|6b| 3.7. order statistics, Beta distributions| plug in formula
|6c| 4. Expectation is linear. Q 5  | 
|7a| 2. Beta distribution | |
|7b| 2. Binomial distribution |
|7c| 3. marginal density | Integration, Beta function| 
|7d| 3. conditional density | | 
|7e| 3. conditional density | |
|8a| 2. Probability  | polar transformation|
|8b| 2. Probability  | polar transformation|
|8c| 3. Definition of independence |