---
title: "Quiz #9"
author: "Milica Cudina"
date: "`r Sys.Date()`"
output: pdf_document
---
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```{r echo=FALSE, warning=FALSE, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  fig.align="center",
  fig.pos="t",
  strip.white = TRUE
)
```
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---

Create an `R`-notebook which prints out the answers to the following problems. Knit the Rmd file into a pdf. Upload the pdf of your solutions onto Canvas. All of your work and calculations **must** be done in `R`.

---

## Problem 1. 
The goal of this exercise is to simulate $10,000$ values from the Pareto distribution using the inverse transform method. Then, you are going to draw a histogram of the simulated values. 

**(4 points)**
Define the function `pareto.inv.cdf` to be the inverse of the cumulative distribution function of the Pareto distribution. 


**(1 point)**
Set the value of the variable `nsim` to be the required number of simulated draws stipulated in the problem statement above. 

**(1 point)** 
Set particular values of a variables `theta` and `alpha` to be the parameters of the two-parameter Pareto distribution you want to simulate from. The values of the parameters you settle upon are completely up to you. 

**(2 points)**
Create the vector `u.s` of `nsim` simulated values from the unit uniform distribution. 

**(4 points)** 
Set the vector `sims` to contain the `nsim` simulated values from the two-parameter Pareto distribution with the parameters `theta` and `alpha` you defined above. 
Do **not** print out the simulated values. 


**(3 points)**
Using the command `hist`, plot the histogram of the simulated values. Note that you can alter bin sizes by using `breaks` in the `hist` inputs.