---
title: "Problem Set 1"
author: "Your Name Here"
date: "2025-04-07"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(fig.align = "center")
library(tidyverse)  # Load any packages you need here
```

## Problem 1: Globe Tossing Posterior Distribution

*Suppose the globe tossing experiment turned out to be 3 water and 11 land. Construct the posterior distribution.*

```{r problem1}
# Your code here
# Hint: You might want to:
# 1. Create a grid of probability values
# 2. Calculate likelihood and prior
# 3. Calculate posterior probability
# 4. Create a plot of the posterior distribution


```

Your interpretation here:


## Problem 2: Posterior Predictive Distribution

*Using the posterior distribution from Problem 1, compute the posterior predictive distribution for the next 5 tosses of the globe.*

```{r problem2}
# Your code here
# Hint: You might want to:
# 1. Sample from your posterior distribution
# 2. Use these samples to simulate new tosses
# 3. Create a visualization of the predictions


```

Your interpretation here:


## Session Information

```{r session-info}
# This will help with debugging and reproducibility
sessionInfo()
```

