# Chapter 3 Sample Codes of Assignment 4

## 3.1 Exercise 1

For this part, you can either submit a html file compiled from .rmd, or a pdf source file generated by .r. All you need to change is

```
# Y00.name0<-"SP500"
# Y00.name0<-"BAC"
# Y00.name0<-"AAPL"
# Y00.name0<-"GE"
```

In other words, define your own `Y00.name0`

variable to the stock that you are interested in. To make sure that there is such stock, you might want to check all the stocks in `casestudy1.data0.00`

, by simply type the following command in the console or code chunk:

`names(casestudy1.data0.00)`

## 3.2 Exercise 3

First you should note that there is no way to let R to find the maximum likelihood estimator (even though that there are some packages that can do this for you). Instead, you should tell R what \(\hat{\theta}_{mle}\) is. In the example file *fm_intro3_gof_rev1.r*, at line `136`

and `137`

, we define what is the mle for our \(\theta\).

```
=sqrt(mean(y^2) - (mean(y))^2) # MLE
std0.mle=IQR(y)/1.3490 # Robust fit std0.robust
```

### 3.2.1 Chi-square goodness-of-fit test

The Chi-Square Goodness-of-Fit (GOF) Test applies to evaluating whether sample data is consistent with coming from a given probablity distribution. The evaluation compares the empirical histogram of the sample data to the theoretical histogram of the given probability distribution.