---
title: "Session 10 — Binomial diplomatic agreements"
author: "Prof. Dae-Jin Lee (daelee@faculty.ie.edu)"
date: "Fall 2026"
output:
  html_document:
    toc: true
    theme: flatly
---

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

Model: 10 independent opportunities, success probability 0.4.

```{r}
set.seed(10)
agreements <- rbinom(10000, size = 10, prob = 0.4)
c(mean = mean(agreements), var = var(agreements))
c(theory_mean = 10 * 0.4, theory_var = 10 * 0.4 * 0.6)
```

```{r}
tibble(agreements = agreements) |>
  ggplot(aes(x = agreements)) +
  geom_histogram(binwidth = 1, boundary = -0.5) +
  labs(
    title = "Simulated Binomial(10, 0.4)",
    x = "Number of agreements",
    y = "Frequency"
  )
```

**Assumptions to say out loud:** fixed $n$, constant $p$, independence.