---
title: "R Problem due Thursday 10/18"
author: "YOUR NAME"
output: pdf_document
---

Acknowledgements: ADD NAMES HERE IF ANYONE ASSISTED YOU.  

**Email knitted pdf file to tleise@amherst.edu by 4pm on the due date.**

## Read Problem 5.6 and section 5.1.2 in Dobrow.

a. Solve 5.6. 

> ANSWER

b. Now suppose Tina only takes 10 courses in the math department. What is the expected number of different professors she will have? (As in part a, assume that every time Tina takes a course, each professor is equally likely to be the instructor). 

> ANSWER

```{r}

```

We want to simulate and verify the results in part b. Recall that there are usually many ways to accomplish a programming task in R, so you might approach this differently than your classmates. Also remember, you don't always need to write a function to accomplish a task. 

Here are some potentially new R commands that may be of use to you. The *unique* command in R will return the unique elements in a vector, which can then be counted up with the *length* command. You can save results too. For example,

```{r}
unique(c(2,2,2,4,4,4,4,4,4,5)) # returns 2, 4, 5
length(unique(c(2,2,2,4,4,4,4,4,4,5))) # returns 3
x<-length(unique(c(2,2,2,4,4,4,4,4,4,5))) # returns x = 3
```

c. Provide pseudocode to outline a reproducible simulation to verify your results in part b. Note that we want to verify the expected value, so you should generate 1000 or 10000 simulated values.

> ANSWER

d. Provide the R code for your reproducible simulation and run it.

> ANSWER

```{r}

```

e. Write a few sentences to compare the mean of your simulated values to the theoretical expected value you calculated in part b. 

> ANSWER


*Acknowledgement: Thank you to Prof Amy Wagaman for sharing this R problem for STAT 360.*