
---
title: "Homework 1 for Stat 340; Introduction to Discrete Random Variables"
author: "Karl Rohe"
date: "1/22/2020"
output: html_document
---

### 1) Use R to generate a single Bernoulli, Binomial, Geometric, and Poisson random variable.

 You can choose the parameter of the distribution to be anything you like.  

Here are the function names: `rbernoulli, rbinom, rgeom, rpois`. Think of the "r" as "generate **R**andom number".

### 1a) What are the 8 headings in each of the help files? 

Reading the help files is hard at first, but it is an essential skill.  Have a look at their help files.  What are the 8 headings?
```{r}
?rbinom
?rgeom
?rpois
```



### 1b) Generate a single copy of each random variable.

```{r}

# generate a single Bernoulli random variable:
library(purrr)
rbernoulli(n = 1, p=.5) 

# generate a single Binomial random variable:
rbinom(n = 1, size = 10, prob = .3)

# generate a single Geometric random variable:

# generate a single Poisson random variable:
```


### 1c) Generate ten copies of each random variable.

```{r}
# generate 10 Bernoulli random variables:
rbernoulli(n = 10, p=.5) 

# generate 10 Binomial random variables:

# generate 10 Geometric random variables:

# generate 10 Poisson random variables:

```


### 2) Make a histogram

One way to think about random variables is through their "distribution".  To see what the distribution of a random variable looks like, generate 10,000 copies of the random variables above and put them in a histogram:

```{r}
# Bernoulli:
hist(rbinom(n = 10000,size = 1,prob = .3))
# or 
library(magrittr)
rbinom(10000,1,.3) %>% hist

# Binomial:

# Geometric:

# Poisson:

```

Repeat the last step, but change the value of the parameter that you put in.  


```{r}
# Bernoulli:
hist(rbinom(10000,1,.3))
# or 
library(magrittr)
rbinom(10000,1,.6) %>% hist

# Binomial:

# Geometric:

# Poisson:

```


### 3)  What happens to the histogram when the parameter gets bigger?  

Answer in words:

1) Bernoulli: The Bernoulli histogram "moves to the right" when the parameter p gets bigger.
2) Binomial:
3) Geometric:
4) Poisson:



### 4) For next week:

Before next week's homework, write down a sequence of heads and tails of length 200 in the code chunk below.  *Make the sequence as random as possible without actually flipping a coin or generating randomv variables on the computer.* Just **try** to make them random by writing them down.
```{r}
# Turn on caps lock and let it rip:
myFlips = "HTHHTHTHTTHH..."
nchar(myFlips)  #make sure it length 200
```
