---
title: "Lab2CodePractice"
author: "Kenya Amano"
date: "10/9/2020"
output: pdf_document
editor_options: 
  chunk_output_type: console
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## Prerequisite
```{r}
# Good practice to remove all objects from the workspace
rm(list = ls())

# Use library() for packages you need, or source() for other R files.
library(tidyverse)

# Setting the seed ensures that we get the same random draw over and over again.
set.seed(20201009)

rnorm(5) # Check
```


## 0. Calculate the following operations by hand (... meaning by R)
a) 
$$ \sum\limits_{i=1}^{5} i = $$
b) 
$$ \prod\limits_{i=1}^{5} i = $$
c) 
$$ 5! \times 10^{3!} \times e^{4} = $$

```{r}

# a) 

# b)

# c)

```



## 1. Build a Bernoulli distribution using the sample() function, where the probability of "success" is 0.7. Run "?sample" if you are unsure how the function works.
```{r}
# Create an imaginary person to flip the coin once for you 
sample(x = 
       )


```

## 2. How do you know if it is working properly? Conduct simulation to check if the assigned probabilities are matached with the empirics 
```{r}


```

## 3. Plot the above Bernoulli distribution
```{r}

```

## 4. Based on the above, generate a binomial distribution, with number of trials equal to 10, without using rbinom()
```{r}
# Create an imaginary person to flip the coin ten times for you

```

## 5. Plot the above binomial distribution
```{r}


```

## 6. Explore the rbinom, dbinom, pbinom functions. What do they do? Answer the following questions:
  a) The probability of a coin landing on head is 0.7. If you were to flip the coin 10 times, what is the probability of getting exactly 7 heads?
  b) What is the probability of getting 7 heads or less?
  c) How do you know (b) is true?
```{r}
# a) Pr(exactly 7 heads) 


# b) Pr(7 heads or less) 


# c) Double check

```