Exploration 2-5.rmd

---
title: "Linear Combinations of Random Variables"
author: "Birgen"
output: html_notebook
---

This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code. 

* Exploration 2.5.1. **Sum of Dice:** Try executing this chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Ctrl+Shift+Enter*. 

```{r}
bluedierolls = sample(c(1, 2, 3, 4, 5, 6), 1000, replace = TRUE, prob = c(1/6, 1/6, 1/6, 1/6, 1/6, 1/6))
greendierolls = sample(c(1, 2, 3, 4, 5, 6), 1000, replace = TRUE, prob = c(1/6, 1/6, 1/6, 1/6, 1/6, 1/6))
diesum=bluedierolls+greendierolls
hist(diesum)
```

Add a new chunk by clicking the *Insert Chunk* button on the toolbar or by pressing *Ctrl+Alt+I*.

When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the *Preview* button or press *Ctrl+Shift+K* to preview the HTML file).

The preview shows you a rendered HTML copy of the contents of the editor. The output of the chunk when it was last run in the editor is displayed.

Run the following code to find the mean and variance of these die rolls
```{r}
mean(diesum)
var(diesum)
```
How do these compare with what you found on the worksheet?

>

* Exploration 2.5.2. **Difference of Dice.** Consider rolling a pair of die, a blue and green one as in Exploration 2.5.1. Let $Z$ denote the difference of the green die subtracted from the blue die ($Z=X_B-X_G$).
Run the following code to simulate 1,000 blue and green die rolls and plot a histogram of their differences.
```{r}
bluedierolls = sample(c(1, 2, 3, 4, 5, 6), 1000, replace = TRUE, prob = c(1/6, 1/6, 1/6, 1/6, 1/6, 1/6))
greendierolls = sample(c(1, 2, 3, 4, 5, 6), 1000, replace = TRUE, prob = c(1/6, 1/6, 1/6, 1/6, 1/6, 1/6))
diediff=bluedierolls-greendierolls
hist(diediff)
```
Run the following code to find the mean and variance of these die rolls.
```{r}
mean(FIXME)
var(FIXME)
```
How do these compare with what you found on the worksheet?

>

* Exploration 2.5.3 **Fast Food Group Order** Last time we worked on fast food orders for one person where customers for a fast food chain have a 40% chance of ordering the regular combo for $\$5$, a 25% chance of ordering the large for $\$7.50$ and a 35% chance of ordering the jumbo for $\$12$. Suppose a group of ten friends order together, and let the cost of their order be $G=X_1+\cdots+X_{10}$ where each $X_i$ is the cost of an individual order. Also, suppose these orders will be independent of each other.

Run the following code to simulate 200 groups of ten and plot a histogram of their purchase amounts.
```{r}
groupcost=rep(0, 200)
  for(i in 1:10){
   groupcost = groupcost+sample(c(5, 7.5, 12), 200, replace = TRUE, prob = c(0.4, 0.25, 0.35))
}
  hist(groupcost)
```
* What does the for(i in 1:10) do in the code?

>

Run the following code to find the mean and variance of the purchase amounts.
```{r}
mean(FIXME)
var(FIXME)
```
How do these compare with what you found on the worksheet?

>

* Exploration 2.5.4 **Ice Cream.** Suppose that a box of Ice Cream comes with on average 60 oz of ice cream, but because theyre not all packed evenly, with a standard deviation of 2 oz. Suppose a scoop of ice cream is 3oz, but with standard deviation of 0.15oz.

Run the following code to simulate 1000 boxes of ice cream with 2 scoops removed.
```{r}
boxoz=rnorm(1000, mean = 60, sd = 2)
scooponeoz=rnorm(1000, mean = 2, sd = .15)
scooptwooz=rnorm(1000, mean = 2, sd = .15)

remainicecream=boxoz-scooponeoz-scooptwooz
hist(remainicecream)
```
* What does boxox simulate?
* What does scooponeoz simulate?
* What does remainicecream simulate?

Create code to find the mean and variance of these remains.
```{r}

```
How do these compare with what you found on the worksheet?

>

* What have you learned today?