---
title: "Problem 8.6c"
author: "Prof. Eric A. Suess"
format:
  html:
    self-contained: true
---

## Problem 8.6c

```{r}
library(fitdistrplus)
```

The data

Simulate $n$ Bernoulli random values with $p = 0.45$.  For the function *fitdist()* to work, we need to have more than one data value.  So one Binomial value is $n$ Bernoulli values. 

```{r}
n <- 1200
size <- 1
prob <- 0.45
x <- rbinom(n, size = size, prob = prob)
head(x)
```

plot the data

```{r}
plotdist(x, discrete =  TRUE, demp = TRUE)
```

fit the data to a binomial distribution to the sample of $n$ Bernoulli values.

```{r}
fit.binom <- fitdist(data = x, dist = "binom",
                     method = "mle",
                     fix.arg = list(size = size),
                     start = list(prob=0.1))

summary(fit.binom)
```

```{r}
plot(fit.binom)
```

compare

```{r}
denscomp(list(fit.binom), legendtext = c("binomial"))
```

plot the log-likelihood

```{r}
llplot(fit.binom)
```