---
title: ''
output: html_document
---

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

##

```{r}
install.packages("ggplot2")
library(ggplot2)
install.packages("fitdistrplus")
library(fitdistrplus)
install.packages("vcd")
library(vcd)
install.packages("goft")
library(goft)

#import and view data set
as_data <- read.csv("~/maths/year 3/S1/Actuarial Statistics MA3206/coursework/as_data.csv")
View(as_data)

#Assigning all variables
gender <- as_data$Gender
H.O <- as_data$H.O
Attendance <- as_data$Attendance
M1 <- as_data$M1
M2 <- as_data$M2
M3 <- as_data$M3
M4 <- as_data$M4
M5 <- as_data$M5
M6 <- as_data$M6
M7 <- as_data$M7
M8 <- as_data$M8
Average <- as_data$Average.Assignment.mark
ME.Mark <- as_data$ME.Mark
MM.Exam <- as_data$MM.Exam
Case.study <- as_data$Case.Study
Overall <- as_data$Overall

#GLM FOR OVERALL MARK

#GAUSSIAN
glm3 <- glm(Overall~gender+H.O+Attendance+Average+ME.Mark+MM.Exam+Case.study, family=gaussian(link="identity"),data = as_data)
glm3
summary(glm3)

#GAMMA
glm3.1 <-glm(Overall~gender+H.O+Attendance+Average+ME.Mark+MM.Exam+Case.study, family=Gamma(link="inverse"),data = as_data)
glm3.1
summary(glm3.1)

#POISSON
glm3.2 <- glm(Overall~gender+H.O+Attendance+Average+ME.Mark+MM.Exam+Case.study, family=poisson(link="log"),data = as_data)
glm3.2
summary(glm3.2)

#BINOMIAL
glm3.3 <- glm(Overall~gender+H.O+Attendance+Average+ME.Mark+MM.Exam+Case.study, family=binomial(link="logit"),data = as_data)

#First we looked at the skewness of the overall module mark

par(mfrow=c(1,1))
plot(density(Overall))
skewness(Overall)

#Plots of poisson, gamma, gaussian for overall module mark

fit_Gaussian <- fitdist(as_data$Overall, "norm", method =c("mle"))
plot(fit_Gaussian)
summary(fit_Gaussian)

ggplot(as.data.frame(as_data$Overall)) +
geom_histogram(mapping=aes(x=as_data$Overall, y=..density..),
colour="white", fill="lightblue")+
ggtitle("Gaussian distribution") +
stat_function(fun = dnorm,
args = list(49.29091, 12.67879

Question 3 (6 points) Let U = { a a b C : a + c = b + d wher...