---
title: "STAT704 Homework Template"
date: "`r Sys.Date()`"
author: John Doe
output: pdf_document
---
```{r setup, include=FALSE, echo=FALSE}
knitr::opts_chunk$set( warning = FALSE, message=FALSE,
                       fig.height = 4, fig.width = 8)
library(knitr)
```

##Problem 1 
Remember to say something to comment on the findings in your analysis. 
To write a mathematical formula in this document, you can do this: $x=\sqrt{3}$ or to have the equation centered: 

$$
f(x; \mu, \sigma)= \frac{1}{\sqrt{2\pi\sigma^2}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}
$$
To learn more about how to write mathematical expressions, google ``write mathematical expressions in latex''.


## Problem 2 
Here is how to create a table in R markdown. 

```{r ktable}
mat<-matrix(1:9, nrow=3)
rownames(mat)<-c("a", "b", "c")
colnames(mat)<-c("n=5", "n=10", "n=30")
kable(mat)
```


## Probelem 3


```{r faithful and iris data}
data(faithful)
data(iris)

##histograms for faithful and iris
par(mfrow=c(1,2))
Hmisc::hist.data.frame(faithful,freq=FALSE)
plot(faithful$eruptions, faithful$waiting, pch=16, main="Old Faithful", xlab="eruption time", ylab="waiting time")
Hmisc::hist.data.frame(iris[,-5],freq=FALSE)
attach(iris)
plot(Sepal.Length, Petal.Length, col=Species)
##boxplots for faithful and iris
par(mfrow=c(1,2))
boxplot(faithful)
boxplot(iris[,-5])
```

##Problem 4


```{r O-ring}
x<-c(0,1,0,NA,0,0,0,0,0,1,1,1,0,0,3,0,0,0,0,0,2,0,1)
table(x[!is.na(x)])
mean(x[!is.na(x)])
```

###Problem 5 

```{r, fig.height=6, fig.width=6}
library(viridis)
image(volcano, col=viridis(200))
```

```{r, fig.height=6, fig.width=6}
library(viridis)
image(volcano, col=viridis(200, option="A"))
```

#### Getting R code from .Rmd file 
Extract R code using purl function
```{r Extract R code, eval=FALSE}
library(knitr)
purl("Stat704_HWtemplate.Rmd")
```


To knit part of your Rmd file, 

`r knitr::knit_exit()`