3-probability_mass_functions.Rmd

---
title: 'Chapter 3: Probability Mass Functions'
author: "Ghislain Nono Gueye, Ph.D."
date: "3/9/2019"
output: bookdown::pdf_document2
---

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

```{r load_packages}
library(dplyr)
library(stringr)
library(purrr)
library(tidyr)
library(ggplot2)

theme_set(theme_minimal())
```


# Probability mass functions (Pmfs)

```{r}
prob_mass_fun <- function(x){
	df <- as.data.frame(prop.table(table(x)))
	colnames(df) <- c("value", "probability")
	df$value <- as.numeric(as.character(df$value))
	df
}

prob_mass_fun <- function(x){
	tibble(value = x) %>%
		group
}

prob_mass_fun(c(1, 2, 2, 3, 5))

```


# The class size paradox

```{r custom_functions}
compute_avg_size <- function(x){
	x %>%
		as.character() %>%
		str_split(pattern = "-") %>%
		map(as.numeric) %>%
		map_dbl(mean)
}

compute_prob <- function(x){
	x / sum(x)
}
```


```{r}
dat <- 
	tibble(
	size = c("5-9", "10-14", "15-19", "20-24", "25-29", "30-34", "35-39", "40-44", "45-49"),
	count = c(8, 8, 14, 4, 6, 12, 8, 3, 2)
	) %>%
	mutate(
		avg_size = compute_avg_size(size),
		prob_size = count / sum(count),
		prob_dean = avg_size * prob_size,
		prob_student = avg_size * prob_dean / sum(prob_dean)
	) %>%
	select(size, avg_size, count, everything())

dat

summarize(dat, avg_class_size_dean = sum(prob_dean), avg_class_size_student = sum(prob_student))
```


```{r}
dat %>%
	select(-size, -count, -prob_size) %>%
	mutate_at(.vars = vars(matches("prob")), .funs = compute_prob) %>%
	gather(key = "prob_type", value = "value", -avg_size) %>%
	
ggplot(aes(x = avg_size, y = value, col = prob_type)) +
	geom_step() +
	labs(x = "Class size", y = "Probability Mass Functon")
```


```{r}
# UnBiasPmf
```


# DataFrame indexing

```{r}

```